Question

x + y= pi/4 , prove (1 + tan x)(1 + tan y)=2

Answer 1

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Here is your answer...✌

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

[ Proved ]

Answer 2

$\huge\mathfrak{Answer}$

Given,

$x + y = \frac{\pi}{4}$

$= > tan(x + y) = tan \frac{\pi}{4}$

$\frac{tanx + tany}{1 - tanx.tany} = 1$

tan x + tan y = 1 - tan x tan y

tan x + tan y + tan x tan y = 1

Adding 1 on both sides

1 + tan x + tan y + tan x tan y = 2

(1+tan x) + tan y (1+tan x)

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==> ( 1+tan x) ( 1+ tan y) = 2

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