2( + )-4 ( + ) +2 ^2 = - Vidyadip

MCQ

$\cos 2(\theta+\phi)-4 \cos (\theta+\phi) \sin \theta \sin \phi+2 \sin ^2 \phi=$

✓
$\cos 2 \theta$
B
$\cos 3 \theta$
C
$\sin 2 \theta$
D
$\sin 3 \theta$

✓

Answer

Correct option: A.

$\cos 2 \theta$

(A)
Putting $\theta=\phi=\frac{\pi}{4}$ in the given expression, we get
$\cos 2\left(\frac{\pi}{2}\right)-4 \cos \left(\frac{\pi}{2}\right) \sin \left(\frac{\pi}{4}\right) \sin \left(\frac{\pi}{4}\right) +2 \sin ^2\left(\frac{\pi}{4}\right)=0$
Put $\theta=\phi=\frac{\pi}{4}$ in option (A), then
$\cos 2 \theta=\cos \frac{\pi}{2}=0$
Hence ontion (A) is the correct answer.

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