Question

If x+y = pi/4 then ( 1 + tan x) (1+ tan y) is equal to

Answer 1

Step-by-step explanation:

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$$\begin{lgathered}x + y = \frac{\pi}{4} \\ \\ \tan(x + y) = \tan\frac{\pi}{4} \\ \\ \frac{ \tan x + \tan y}{1 - \tan x \tan y} = 1 \\ \\ \tan x + \tan y = 1 - \tan x \tan y \\ \\ \tan x + \tan y + \tan x \tan y = 1 \\ \\ Adding \: \: 1 \: \: both \: sides \: \\ We\: get,\\ \\ 1 + \tan x + \tan y + \tan x \tan y = 1 + 1 \\ \\ (1 + \tan x) + \tan y (1+ \tan x) = 2 \\ \\ (1+ \tan x) (1+ \tan y) = 2\end{lgathered}$$

[ Proved ]

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