First slide

Compound angles

Question

If $\cos (A - B) = 3 / 5 and \tan Atan B = 2,$ then

Moderate

A

$\cos Acos B = 1 / 5$
B

$\sin Asin B = - 2 / 5$
C

$\cos Acos B = - 1 / 5$
D

$\sin Asin B = - 1 / 5$

Solution

$\cos (A - B) = \frac{3}{5}$
$or 5 \cos Acos B + 5 \sin Asin B = 3 - - - - (i)$
From the second relation, we have
$\begin{array}{l} \sin Asin B = 2 \cos Acos B - - - (ii) \\ \Rightarrow \cos Acos B = \frac{1}{5} and \sin Asin B = \frac{2}{5} \end{array}$

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