Given that ( - 2 ) = 2 ( + B 2 ), then 2 2 is equal to - Vidyadip

MCQ

Given that $\cos \left( {\frac{{\alpha - \beta }}{2}} \right) = 2\cos \left( {\frac{{\alpha + B}}{2}} \right)$, then $\tan \frac{\alpha }{2}\tan \frac{\beta }{2} $ is equal to

A
$\frac{1}{2}$
✓
$1\over3$
C
$\frac{1}{4}$
D
$\frac{1}{8}$

✓

Answer

Correct option: B.

$1\over3$

b
(b) $\cos \left( {\frac{{\alpha - \beta }}{2}} \right) = 2\cos \left( {\frac{{\alpha + \beta }}{2}} \right)$

==> $\cos \frac{\alpha }{2}\cos \frac{\beta }{2} + \sin \frac{\alpha }{2}\sin \frac{\beta }{2} = 2\cos \frac{\alpha }{2}\cos \frac{\beta }{2} - 2\sin \frac{\alpha }{2}\sin \frac{\beta }{2}$

$ \Rightarrow 3\sin \frac{\alpha }{2}\sin \frac{\beta }{2} = \cos \frac{\alpha }{2}\cos \frac{\beta }{2}$

==> $\tan \frac{\alpha }{2}\tan \frac{\beta }{2} = \frac{1}{3}$.

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