Question

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

• A. $ \cos \, A \, \cos \, B = \frac{1}{5}$
• B. $ \sin \, A \, \sin \, B = -\frac{2}{5}$
• C. $ \cos (A + B) = \frac{1}{5}$
• D. $ \sin \, A \, \sin \, B = \frac{4}{5}$

Answer 1

Answer: (A)

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