If sin ⁡ (A+B ) sin ⁡ (A-B )+ cos ⁡ (A+B ) cos ⁡ (A-B )= 12 and 0

Question

If sin ⁡ (A+B ) sin ⁡ (A-B )+ cos ⁡ (A+B ) cos ⁡ (A-B )= 12 and 0<B< 2, then B=

Accepted Answer

Correct answer: A. (a) Given sin ⁡ (A+B ) sin ⁡ (A-B )+ cos ⁡ (A+B ) cos ⁡ (A-B )= 12 Apply cos ⁡ (x-y )= cos ⁡ xcos ⁡y+ sin ⁡ xsin ⁡y ⇒ cos ⁡ (A+B-A+B )= 12 cos ⁡ (2B )= 12= cos ⁡ 3 ⇒2B= 3 ⇒B= 6

$If sin (A + B) sin (A - B) + cos (A + B) cos (A - B) = \frac{1}{2} and 0 < B < \frac{π}{2}, then B =$

Solution

More Trigonometric Ratios & Identities PYQs