Painless Trigonometry: (December 14 – December 21, 2013)

 

Sum of tangents

Given:

tan(x) + tan(y) = 4

cot(x) + cot(y) = 5

Find the value of  tan(x+y)

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1. Arsh Singh. yourmathguru.com

2. Muthu Krishna.Kle college , Bengaluru

3. Jeffry Robles, University of the Philippines – Diliman

4. K.Rahul Mohideen

5. Spandan B, Pace Jr. Science College, India

6. Sebastian Pimber. Colombia

7. Kennard Ong Sychingping. De La Salle University

8.Jhay Dela Cruz. PUP-Taguig

9. Kenny Wong, Jurong Junior College, Singapore

10. Erick Ocampo- Manila Science High School

11. Jia Syuen- SMJK Sam Tet, Malaysia

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

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8 Responses

  1. K.Rahul Mohideen says:

    tan(x)+tan(y)=4
    1/tan(x)+1/tan(y)=5 => tan(x).tan(y)=(tan(x)+tan(y))/5 =>tan(x).tan(y)=4/5
    tan(x+y)=(tan(x)+tan(y))/(1-tan(x).tan(y))
    tan(x+y)=4/(1-4/5)
    tan(x+y)=20

  2. Spandy says:

    Spandan B, Pace Jr. Science College, India-
    tan(x) +tan(y)/ tan(x)tan(y)=5
    Thus, tan(x)tan(y)=4/5…
    tan(x+y)=20

  3. Jhay Dela Cruz says:

    20

    Pup-taguig

  4. Jia Syuen- SMJK Sam Tet, Malaysia says:

    -1/2

  5. Jia Syuen- SMJK Sam Tet, Malaysia says:

    tan(x + y) = (tan(x) + tan(y))/(1 – tan(x)tan(y))
    = 4/(1 – (tan(y) + tan(x))/(cot(x) + cot(y)))
    = 4/(1 – 4/5)
    = 20.

  6. joven19 says:

    1/ tan x + 1/tan y = 5
    (tan x + tan y) / ( tan x)(tan y)= 5

    4 / (tan x)(tan y) = 5
    (tan x)(tan y) = 4/5

    tan (x+y ) = (tan x + tan y) / [ 1 – (tan x)(tan y)
    tan (x+y) = 4 / [ 1 – 4/5]
    tan(x+y) = 4 / (1/5) = 20

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