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Question
If cos (A − B) \[= \frac{3}{5}\] and tan A tan B = 2, then
Options
- \[\cos A \cos B = \frac{1}{5}\]
- \[\cos A \cos B = - \frac{1}{5}\]
- \[\sin A \sin B = - \frac{1}{5}\]
- \[\sin A \sin B = - \frac{1}{5}\]
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Solution
\[\tan A \tan B=\frac{\sin A \sin B}{\cos A \cos B}=2 \left( \text{Given }\right) . . . (1)\]
Also,
\[\cos(A - B) = \frac{3}{5}\]
\[ \Rightarrow \cos A \cos B + \sin A \sin B = \frac{3}{5}\]
\[\therefore \sin A \sin B = \frac{3}{5} - \cos A\cos B . . . (2) \]
\[\text{ Substituting eq (2) in eq (1), we get:}\]
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