Question

If sinA + sinB = a, cosA – cosB = b, then the value of cos (A – B) is

(a) \(\frac{2ab}{a^2+b^2}\)

(b) \(\frac{2ab}{a^2-b^2}\)

(c) \(\frac{a^2-b^2}{a^2+b^2}\)

(d) \(\frac{a^2+b^2}{a^2-b^2}\)

Answer 1

(c) \(\frac{a^2-b^2}{a^2+b^2}\)

sin A + sin B = a

(∵ sin (– θ) = – sin θ) 

Dividing eqn (ii) by eqn (i), we get