If (A - B) = 3 5 and A B = 2, then - Vidyadip

MCQ

If $\cos (A - B) = \frac{3}{5}$ and $\tan A\tan B = 2,$ then

✓
$\cos A\cos B = \frac{1}{5}$
B
$\sin A\sin B = - \frac{2}{5}$
C
$\cos A\cos B = - \frac{1}{5}$
D
$\sin A\sin B = - \frac{1}{5}$

✓

Answer

Correct option: A.

$\cos A\cos B = \frac{1}{5}$

a
(a) $\cos \,(A - B) = \frac{3}{5}$

$\therefore$ $5\,\,\cos A\,\,\cos B + 5\,\,\sin A\,\,\sin B = 3$…..$(i) $

From $2^{nd}$ relation, $\sin A\sin B = 2\cos A\cos B$ .....$(ii)$

$\therefore $ $\cos A\cos B = \frac{1}{5}$

and $5\,\left( {\frac{1}{2} + 1} \right)\,\sin A\,\,\sin B = 3$.

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