MCQ
$2\,{\sin ^2}\beta + 4\,\,\cos \,(\alpha + \beta )\,\,\sin \,\alpha \,\sin \,\beta + \cos \,2\,(\alpha + \beta ) = $
- A$\sin \,\,2\alpha $
- B$\cos \,\,2\beta $
- ✓$\cos \,\,2\alpha $
- D$\sin \,\,2\beta $
$2{\sin ^2}\beta = 1 - \cos 2\beta $
$L.H.S.$ $ = - \cos 2\beta + 2\cos (\alpha + \beta )\,[2\sin \alpha \sin \beta + \cos (\alpha + \beta )]$
$ = - \cos 2\beta + 2\cos (\alpha + \beta )\cos (\alpha - \beta )$
$ = - \cos 2\beta + (\cos 2\alpha + \cos 2\beta ) = \cos 2\alpha $.
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