# 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  $tan(x+y)$

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

### 7 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