If ^2 =2 ^2 +1, then 2 + ^2 equals - Vidyadip

MCQ

If $\tan ^2 \theta=2 \tan ^2 \phi+1$, then $\cos 2 \theta+\sin ^2 \phi$ equals

A
-1
✓
$0$
C
1
D
2

✓

Answer

Correct option: B.

$0$

(B)
$\tan ^2 \theta=2 \tan ^2 \phi+1$
$\Rightarrow 1+\tan ^2 \theta=2\left(1+\tan ^2 \phi\right)$
$\Rightarrow \sec ^2 \theta=2 \sec ^2 \phi$
$\Rightarrow \cos ^2 \phi=2 \cos ^2 \theta$
$\Rightarrow \cos ^2 \phi=1+\cos 2 \theta$
$\Rightarrow \sin ^2 \phi+\cos 2 \theta=0 \ldots\left[\because \sin ^2 \theta+\cos ^2 \theta=1\right]$

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