If 2 + 2 = 1/2 and 2 + 2 = 3/2, then ^2 ( - ) = - Vidyadip

MCQ

If $\sin 2\theta + \sin 2\phi = 1/2$ and $\cos 2\theta + \cos 2\phi = 3/2$, then ${\cos ^2}(\theta - \phi ) = $

A
$3/8$
✓
$5/8$
C
$3/4$
D
$5/4$

✓

Answer

Correct option: B.

$5/8$

b
(b) Given, $\sin 2\,\theta + \sin 2\phi = 1/2$…..$(i)$

and $\cos 2\,\theta + \cos 2\,\varphi = 3/2$…..$(ii)$

Square અને adding ,

$\therefore \,({\sin ^2}2\theta + {\cos ^2}2\theta ) + ({\sin ^2}2\phi + {\cos ^2}2\phi )$

$ + 2\,[\sin 2\,\theta \,\sin 2\,\phi + \cos 2\,\theta \,\cos 2\,\phi ] = 1/4 + 9/4$

==> $\cos 2\theta \cos 2\,\phi + \sin 2\theta \sin 2\phi = 1/4$

==> $\cos (2\theta - 2\phi ) = 1/4$

==> ${\cos ^2}(\theta - \phi ) = 5/8$.

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