NIMCET 2024 Paper

Section: Mathematics

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Question : 19 of 120

Marks: +1, -0

The value of

\tan (\;{π}/{4}+θ) \tan (\;{3 π}/{4}+θ)

is:

-2
2
1
-1

Solution:

\;\;\text " Using the formula "\; \tan (x+y)=\;{\tan x+\tan y}/{1-\tan x \tan y}

\;\;{\tan {π}/{4}+\tan θ}/{1-\tan \;{π}/{4} \tan θ} × \;{\tan {3 π}/{4}+\tan θ}/{1-\tan \;{3 π}/{4} \tan θ}

\;=\;{1+\tan θ}/{1-\tan θ} × \;{-1+\tan θ}/{1+\tan θ}=-1

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