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Question
If cos(A – B) = `3/5` and tan A tan B = 2, then ______.
Options
cos A cos B = `1/5`
sin A sin B = `-2/5`
cos A cos B = `-1/5`
sin A sin B `-1/5`
MCQ
Fill in the Blanks
Solution
If cos(A – B) = `3/5` and tan A tan B = 2, then `underlinebb(sin A sin B = -2/5)`.
Explanation:
cos(A – B) = `3/5`
∴ 5 cos A cos B + 5 sin A sin B = 3 ...(i)
From 2nd relation,
sin A sin B = 2 cos A cos B ...(ii)
∴ cos A cos B = `1/5` and `5(1/2 + 1)` sin A sin B = 3
sin A sin B = `-2/5`
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Trigonometric Functions of Sum and Difference of Angles
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