Question

If sin A + sin B = a and cos A + cos B = b. show that
tan (A + B) = 2ab/b^2-a^2​

Answer 1

Answer:

solved below

Step-by-step explanation:

sin A + sin B = a and cos A + cos B = b

(sin A + sin B)² = a²

(cos A + cos B)² = b ²

1 + 2 cos A cos B  =  b²

1 + 2 sin A sin B  =  a²

2cos (A + B) = b² - a²

cos (A + B) = (b² - a²)/2 = k

sin (A + B) = √ 1 - k²

tan (A + B) = √ 1 - k² /k = {√ 1 - (b² - a²)²/4} ÷ (b² - a²)/2