Question

If (x-y)=π/4.Prove that (1+tanx)(1+tany)=2tanx

Answer 1

Answer:

hope this solution helps u

Answer 2

Given : $x-y =\frac{\pi}{4}$

To prove : $(1+\tan x)(1+\tan y)= 2\tan x$

Explanation:

$x-y =\frac{\pi}{4}..(1)\\\\(1+\tan x)(1+\tan y)\\\\1+\tan y +\tan x+\tan x \tan y..(2) \\\\\text{multiply by tan in equation 1}\\\\\tan (x-y)= \tan \frac{\pi}{4}\\\\ \frac{\tan x -\tan y }{1+\tan x\tan y}= 1\\\\\tan x - \tan y = 1+\tan x \tan y\\\\\tan x =1+\tan y + \tan x \tan y\\\\\text{add both side tan x }\\\\\tan x+\tan x =1+\tan y + \tan x \tan y+\tan x \\\\\text {using 2}\\\\2\tan x = (1+\tan x)(1+\tan y)$

hence proved

#Learn more :

https://brainly.in/question/5159697