Identity Index in Trigonometry

Here is the formula index in trigonometric identities. Again, identities are the fundamentals of trigonometry. This is the counterpart of four basic operations in arithmetic.

Basic Identity

sinx=\displaystyle\frac{1}{cscx}

cosx=\displaystyle\frac{1}{secx}

tanx=\displaystyle\frac{1}{cotx}

Pythagorean Identity

cos^2x+sin^2x=1

sec^2x=1+tan^2x

csc^2x=1+cot^2x

Addition and Subtraction Identify

cos(x+y)=cosxcosy-sinxsiny

cos(x-y)=cosxcosy+sinxsiny

sin(x+y)=sinxcosy+cosxsiny

sin(x-y)=sinxcosy-cosxsiny

tan(x+y)=\displaystyle\frac{tanx+tany}{1-tanxtany}

tan(x-y)=\displaystyle\frac{tanx-tany}{1+tanxtany}

cot(x+y)= \displaystyle\frac{cotxcoty-1}{cotx+coty}

cot(x-y)= \displaystyle\frac{cotxcoty+1}{cotx-coty}

Special Reduction Identity

sin(-x)=-sinx

cos(-x)=cosx

tan(-x)=-tanx

cot(-x)=-cotx

cos(\frac{\pi}{2}-x)=cosx

sin(\frac{\pi}{2}-x)=sinx

tan(\frac{\pi}{2}-x)=tanx

cot(\frac{\pi}{2}-x)=cotx

Double Angle Identity

sin2x=2sinxcosx

cos2x=cos^2x-sin^2x=1-2sin^2x=2sin^2x-1

tan2x=\displaystyle\frac{2tanx}{1-tan^2x}

Half Angle Identity

sin(\displaystyle\frac{x}{2})=\pm\sqrt{\displaystyle\frac{1-cosx}{2}}

cos(\displaystyle\frac{x}{2})=\pm\sqrt{\displaystyle\frac{1+cosx}{2}}

tan(\displaystyle\frac{x}{2})=\displaystyle\frac{sinx}{1+cosx}=\pm\sqrt{\displaystyle\frac{1-cosx}{1+cosx}}

Product to Sum Identity

sinxcosy=\displaystyle\frac{1}{2}[sin(x+y)+sin(x-y)]

cosxsiny=\displaystyle\frac{1}{2}[sin(x+y)-sin(x-y)]

cosxcosy=\displaystyle\frac{1}{2}[cos(x+y)+cos(x-y)]

sinxsiny=\displaystyle\frac{1}{2}[cos(x-y)-sin(x+y)]

Sum to Product Identity

sinx+siny=2sin\displaystyle\frac{x+y}{2}\cdot cos\displaystyle\frac{x-y}{2}

sinx-siny=2cos\displaystyle\frac{x+y}{2}\cdot sin\displaystyle\frac{x-y}{2}

cosx+cosy=2cos\displaystyle\frac{x+y}{2}\cdot cos\displaystyle\frac{x-y}{2}

cosx-cosy=-2sin\displaystyle\frac{x+y}{2}\cdot sin\displaystyle\frac{x-y}{2}

If you want to add more, feel free to add in comment box and I’m glad to include that.

 

 

 

 

 

 

 

Dan

Dan

Blogger and a Math enthusiast. Has no interest in Mathematics until MMC came. Aside from doing math, he also loves to travel and watch movies.
Dan

Latest posts by Dan (see all)

You may also like...

119 Responses

  1. bpc9on This particular blog is without a doubt entertaining additionally diverting. I have picked a lot of helpful advices out of this source. I ad love to go back over and over again. Thanks a bunch!

  2. Thanks for sharing, this is a fantastic blog.Really looking forward to read more. Much obliged.

  3. Dramacool says:

    I truly appreciate this blog article.Thanks Again. Really Great.

  4. I truly appreciate this post.Really looking forward to read more. Awesome.

  5. London tours says:

    Major thankies for the post.Really looking forward to read more. Keep writing.

  6. Thanks again for the article post.Thanks Again. Much obliged.

  7. Ultimately, a problem that I am passionate about. I ave looked for details of this caliber for your previous a number of hours. Your site is significantly appreciated.

  8. This is a really good tip particularly to those new to the blogosphere. Short but very accurate information Thank you for sharing this one. A must read article!

  9. You can certainly see your expertise in the work you write. The world hopes for more passionate writers such as you who aren at afraid to mention how they believe. All the time follow your heart.

  10. Wow, this piece of writing is good, my sister is analyzing such things, so I am going to let know her.

  11. dji says:

    Wow, great article.Really thank you! Awesome.

  12. This really answered my problem, thank you!

  13. There is certainly a great deal to learn about this topic. I really like all the points you ave made.

  14. candles says:

    pris issue a ce, lettre sans meme monde me

  15. UoN says:

    Thank you ever so for you article.Really looking forward to read more. Keep writing.

  16. Cheap jacket says:

    xrumer ??????30????????????????5??????????????? | ????????

  17. 123movies.to says:

    This website was how do you say it? Relevant!! Finally I have found something which helped me. Thank you!

  18. Really appreciate you sharing this post.Really thank you! Keep writing.

  19. Thanks again for the blog.Really looking forward to read more. Fantastic.

  20. Really appreciate you sharing this blog post.Really thank you! Much obliged.

  21. Really appreciate you sharing this post. Awesome.

  22. Thanks a lot for the blog article.Really thank you!

  23. Major thankies for the blog post.Really thank you! Really Great.

  24. amiclubwear says:

    Thanks for sharing, this is a fantastic blog.Thanks Again. Will read on…

  25. fallen angel says:

    That is a really good tip particularly to those new to the blogosphere. Brief but very accurate information Appreciate your sharing this one. A must read article!

  26. Thank you ever so for you blog post.Really looking forward to read more. Want more.

  27. cookware says:

    standard parts you happen to be familiar with but might not know how to utilize properly, along with other unique offerings in the car that ensure it is more hard to.

  28. A round of applause for your post.Thanks Again. Keep writing.

  29. Thanks for sharing, this is a fantastic post.Much thanks again. Keep writing.

  30. I value the post.Much thanks again. Really Cool.

  31. Photography says:

    Very informative article post.Really looking forward to read more. Awesome.

  32. Friv says:

    Wow, great blog article.Really looking forward to read more. Will read on

  33. school says:

    Hey, thanks for the blog. Really Great.

  34. It as hard to find well-informed people for this subject, however, you seem like you know what you are talking about! Thanks

  35. Fantastic blog article.Thanks Again. Awesome.

  36. You ave made some decent points there. I checked on the web to find out more about the issue and found most individuals will go along with your views on this web site.

  37. Maintenance says:

    Thanks-a-mundo for the article. Cool.

  38. understand this topic. You understand a whole lot its almost hard to argue with you (not that I really would want toHaHa).

  39. Utterly indited subject material, Really enjoyed studying.

  40. Well I definitely liked studying it. This post procured by you is very practical for good planning.

  41. wonderful points altogether, you simply gained a new reader. What would you suggest in regards to your post that you made a few days ago? Any positive?

  42. Perfect work you have done, this internet site is really cool with great info.

  43. I truly appreciate this blog post. Keep writing.

  44. you are really a good webmaster. The website loading speed is amazing. It seems that you are doing any unique trick. Also, The contents are masterpiece. you have done a excellent job on this topic!

  45. Wow I\ ave been looking and waiting for this a quite sometime. The topics are good and i know i will learn so much for this. Thank you so much and happy new year business English pod.

  46. Thank you ever so for you article. Great.

  47. louis vuitton travel case ??????30????????????????5??????????????? | ????????

  48. I went over this website and I believe you have a lot of good info, saved to fav (:.

  49. It was really informative. Your site is extremely helpful.

  50. This is my first time go to see at here and i am in fact impressed to read everthing at single place.

  51. Wohh just what I was looking for, thanks for putting up.

  52. I am so grateful for your article post.Much thanks again. Want more.

  53. I value the blog post.Really looking forward to read more. Want more.

  54. These kind of post are always inspiring and I prefer to read quality content so I happy to find many good point here in the post

  55. Collen says:

    the primary way to maximize SEO for a web site.

  56. Entry-level says:

    Say, you got a nice blog post.

  57. Melva says:

    Your style is so unique compared to other people I ave read stuff from. I appreciate you for posting when you have the opportunity, Guess I will just book mark this page.

  58. I appreciate you sharing this blog post.Much thanks again. Keep writing.

  59. Artist says:

    Well I really liked reading it. This article provided by you is very useful for accurate planning.

  60. Im grateful for the blog.Really thank you! Fantastic.

  61. EDM says:

    I am so grateful for your blog article.Thanks Again. Great.

  62. msp vip hack says:

    Unfortunately, fanminds did not present at the GSummit, so their slides are not included. I\ ad love to hear more about their projects. Please get in touch! Jeff at gamification dot co

  63. You make it entertaining and you still care for to stay it sensible.

  64. This is really interesting, You are a very skilled blogger. I have joined your feed and look forward to seeking more of your great post. Also, I ave shared your site in my social networks!

  65. This very blog is obviously awesome and also informative. I have chosen a lot of interesting things out of this amazing blog. I ad love to return over and over again. Thanks a bunch!

  66. It is really a nice and helpful piece of information. I am glad that you shared this helpful information with us. Please keep us up to date like this. Thank you for sharing.

  67. Im obliged for the blog.Much thanks again. Want more.

  68. Thanks for another excellent article. Where else could anyone get that type of info in such an ideal way of writing? I ave a presentation next week, and I am on the look for such information.

  69. Very excellent info can be found on web site.

  70. informatii interesante si utile postate pe blogul dumneavoastra. dar ca si o paranteza , ce parere aveti de cazarea la particulari ?.

  71. to read more says:

    The Birch of the Shadow I believe there may be a couple of duplicates, but an exceedingly useful listing! I have tweeted this. Many thanks for sharing!

  72. Very good info. Lucky me I discovered your website by chance (stumbleupon). I have saved it for later!

  73. A round of applause for your article. Really Great.

  74. click here says:

    It as especially a abundant as thriving as practical a part of details. I will live thankful that you just free this type of information as anyway as us all.

  75. more details says:

    It is best to take part in a contest for among the best blogs on the web. I all suggest this website!

  76. Precisely what I was looking for, thankyou for posting.

  77. jav online says:

    Thank you for your post.Really thank you! Cool.

  78. flexvit says:

    This awesome blog is really interesting and informative. I have discovered a lot of interesting stuff out of this amazing blog. I ad love to visit it every once in a while. Thanks a lot!

  79. I see something truly special in this site.

  80. This is one awesome blog post.Really thank you! Really Great.

  81. I really liked your blog post.Really thank you! Keep writing.

  82. Oh my goodness! an amazing article. Great work.

  83. Say, you got a nice article post.Really looking forward to read more.

  84. you ave got an awesome weblog here! would you like to make some invite posts on my weblog?

  85. This is one awesome blog post.Really looking forward to read more. Much obliged.

  86. scar treatment for acne scar treatment lotion scar treatment

  87. Marketing says:

    Wow! This could be one particular of the most beneficial blogs We have ever arrive across on this subject. Actually Great. I am also a specialist in this topic so I can understand your hard work.

  88. Thanks, However I am having difficulties with

  89. Thanks again for the blog article.Really thank you! Cool.

  90. There is perceptibly a bunch to know about this. I suppose you made certain nice points in features also.

  91. It is usually a very pleased day for far North Queensland, even state rugby league usually, Sheppard reported.

  92. Lauretta says:

    Usually I do not read post on blogs, but I would like to say that this write-up very compelled me to check out and do it! Your writing taste has been amazed me. Thank you, very nice article.

  93. Just a smiling visitant here to share the love (:, btw great style and design.

  94. Pretty! This was an incredibly wonderful post. Many thanks for supplying this information.

  95. I’а†ve recently started a blog, the info you offer on this web site has helped me greatly. Thanks for all of your time & work.

  96. pretty practical material, overall I feel this is well worth a bookmark, thanks

  97. Really enjoyed this article post.Really looking forward to read more. Really Great.

  98. click here says:

    Thanks again for the blog article.Really looking forward to read more. Cool.

  99. I really enjoy the blog post.

  100. vape says:

    I think this is a real great post.Thanks Again. Fantastic.

  101. This is very interesting, You are a very skilled blogger. I ave joined your rss feed and look forward to seeking more of your wonderful post. Also, I have shared your web site in my social networks!

  102. Thanks a lot for the article post. Cool.

  103. click here says:

    Way cool! Some extremely valid points! I appreciate you writing this post plus the rest of the site is very good.

  104. Muchos Gracias for your article post. Really Great.

  105. App web says:

    This is a good tip especially to those new to the blogosphere. Simple but very accurate info Thank you for sharing this one. A must read article!

  106. click here says:

    This very blog is no doubt interesting as well as amusing. I have picked up a bunch of useful advices out of this blog. I ad love to go back every once in a while. Thanks!

  107. Wow, great post.Really looking forward to read more. Really Cool.

  108. Say, you got a nice blog.Really thank you!

  109. Great post.Really looking forward to read more. Keep writing.

  110. wow, awesome post.Really thank you! Much obliged.

  111. I appreciate you sharing this blog.Really thank you! Awesome.

  112. Muchos Gracias for your post.Really thank you! Awesome.

  113. Thanks so much for the article. Keep writing.

  114. You are my inhalation, I have few blogs and occasionally run out from brand . Truth springs from argument amongst friends. by David Hume.

  115. Fantastic blog article.Really looking forward to read more. Much obliged.

  116. Really enjoyed this blog post.Really looking forward to read more.

  117. If you are interested to learn Web optimization techniques then you have to read this article, I am sure you will obtain much more from this article on the topic of Web optimization.

  118. Major thankies for the post.Much thanks again. Awesome.

  119. You could definitely see your skills in the work you write. The world hopes for even more passionate writers like you who are not afraid to say how they believe. Always follow your heart.

Leave a Reply

Your email address will not be published.