( 4 + ) (3 4 + )is equal to - Vidyadip

MCQ

$\tan\left(\frac{\pi}{4}+\theta\right)\tan\left(\frac{3\pi}{4}+\theta\right)$is equal to

A
-2
✓
-1
C
1
D
$0$

✓

Answer

Correct option: B.

-1

(B)
$\tan\left(\frac{\pi}{4}+\theta\right)\tan\left(\frac{3\pi}{4}+\theta\right)$
$=\tan\left(\frac{\pi}{4}+\theta\right)\tan\left(\frac{\pi}{2}+\left(\frac{\pi}{4}+\theta\right)\right)$
$=\tan\left(\frac{\pi}{4}+\theta\right)\left\{-\cot\left(\frac{\pi}{4}+\theta\right)\right\}$
$\ldots\left[\because\tan\left(\frac{\pi}{2}+\alpha\right)=-\cot\alpha\right]$
$=-1$

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