2 2 + ^2( - )- ^2( + ) is equal to: [ Hint: Use ^2A- ^2B= (A+B) (… - Vidyadip

MCQ

$\cos2\theta\cos2\phi+\sin^2(\theta-\phi)-\sin^2(\theta+\phi)$ is equal to:
$[$Hint: Use $\sin^2\text{A}-\sin^2\text{B}=\sin(\text{A+B})\sin(\text{A}-\text{B})]$

A
$\sin2(\theta+\phi)$
✓
$\cos2(\theta+\phi)$
C
$\sin2(\theta-\phi)$
D
$\cos2(\theta-\phi)$

✓

Answer

Correct option: B.

$\cos2(\theta+\phi)$

$\cos2\theta\cos2\phi+\sin^2(\theta-\phi)-\sin^2(\theta+\phi)$
$=\cos2\theta\cos2\phi+\sin(\theta-\phi+\theta+\phi)\sin(\theta-\phi-\theta-\phi)$
$=\cos2\theta\cos2\phi-\sin2\theta\sin2\phi$
$=\cos(2\theta+2\phi)$
$=\cos2(\theta+\phi)$

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