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 $\sin A\sin B=2\cos A\cos B$
$\Rightarrow 3\cos A\cos B=\frac{3}{5}\Rightarrow \cos A\cos B=\frac{1}{5}$