Question

If cos(A – B) = `3/5` and tan A tan B = 2, then ______.

विकल्प

• cos A cos B = `1/5`

• sin A sin B = `-2/5`

• cos A cos B = `-1/5`

• sin A sin B `-1/5`

Answer 1

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`