If  cos(a - b) = $$\frac12$$​ and sin(a + b) = 1 then find a.

Correct option is A

Given:

sin (a + b) = 1 and cos (a - b) = 1/2

Solution:

$$\sin (a + b) = 1 \\\sin (a + b) = \sin \, 90^\circ \\ \Rightarrow a + b = 90^\circ \, \text{-} \, (i) \\\ \text{and} \, \cos (a - b) = \frac{1}{2} \\\ \\ \cos (a - b) = \cos \, 60^\circ \\\ \\ \Rightarrow a - b = 60^\circ \, \text{-} \, (ii) \\\ \text{add eq}^n \, (i) \, \text{and} \, (ii) \\\ \ \ 2a = 150^\circ \\\ \\ \Rightarrow a = 75^\circ$$​