If cos⁡(A−B)=35 and tan⁡ Atan⁡B=2 then

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

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

Solution:

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

or $5 \cos Acos B + 5 \sin Asin B = 3$ ------------(1)

From the second relation , we get

$\begin{array}{l} \sin Asin B = 2 \cos Acos B - - - - - (2) \\ \Rightarrow \cos Acos B = \frac{1}{5} and \sin Asin B = \frac{2}{5} \end{array}$

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