- Home
- Standard 11
- Mathematics
3.Trigonometrical Ratios, Functions and Identities
medium
$2\,{\sin ^2}\beta + 4\,\,\cos \,(\alpha + \beta )\,\,\sin \,\alpha \,\sin \,\beta + \cos \,2\,(\alpha + \beta ) = $
A
$\sin \,\,2\alpha $
B
$\cos \,\,2\beta $
C
$\cos \,\,2\alpha $
D
$\sin \,\,2\beta $
(IIT-1977)
Solution
(c) $\cos 2(\alpha + \beta ) = 2{\cos ^2}(\alpha + \beta ) – 1,$
$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 $.
Standard 11
Mathematics
