Question

prove that tan^x+tan^y=tan^x+y/1-xy​

Answer 1

Hello!!!

Hey my dear friend here is your answer_____________

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

We already know (see trigonometry identities) that

cos (x+y) = cos x cos y - sin x sin y

and

sin (x+y) = sin x cos y + cos x sin y

So,

tan (x + y) = (sin x+y) / (cos x+y)

= (sin x cos y + cos x sin y) / (cos x cos y - sin x sin y)

Dividing both numerator and denominator by (cos x)(cos y), we get:

= ( sin x / cos x + sin y / cos y) / (1 - sin x sin y/(cos x cos y))

= (tan x + tan y) / (1 - tan x tan y).

Hence, the prof.

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Refer attached pic...

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Hope this answer will help you....