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3.Trigonometrical Ratios, Functions and Identities
easy
If $\tan \beta = \cos \theta \tan \alpha ,$ then ${\tan ^2}\frac{\theta }{2} = $
A
$\frac{{\sin (\alpha + \beta )}}{{\sin (\alpha - \beta )}}$
B
$\frac{{\cos (\alpha - \beta )}}{{\cos (\alpha + \beta )}}$
C
$\frac{{\sin (\alpha - \beta )}}{{\sin (\alpha + \beta )}}$
D
$\frac{{\cos (\alpha + \beta )}}{{\cos (\alpha - \beta )}}$
Solution
(c) ${\tan ^2}\frac{\theta }{2} = \frac{{1 – \cos \theta }}{{1 + \cos \theta }} $
$= \frac{{\tan \alpha – \tan \beta }}{{\tan \alpha + \tan \beta }} $
$= \frac{{\sin (\alpha – \beta )}}{{\sin (\alpha + \beta )}}$.
Standard 11
Mathematics
