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3.Trigonometrical Ratios, Functions and Identities
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If $\sin 2\theta + \sin 2\phi = 1/2$ and $\cos 2\theta + \cos 2\phi = 3/2$, then ${\cos ^2}(\theta - \phi ) = $
A
$3/8$
B
$5/8$
C
$3/4$
D
$5/4$
Solution
(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$
==> $\cos 2\theta \cos 2\,\phi + \sin 2\theta \sin 2\phi = 1/4$
==> $\cos (2\theta – 2\phi ) = 1/4$
==> ${\cos ^2}(\theta – \phi ) = 5/8$.
Standard 11
Mathematics
