If sin A + cos A = 1 then sin 2A is equal to: (a) 1 (b) 2 (c) 0 (d) 1/2

Question

If sin A + cos A = 1 then sin 2A is equal to: 

(a) 1 

(b) 2 

(c) 0 

(d) \(\frac{1}{2}\)

Answer 1

(c) 0

Given sin A + cos A = 1 

Squaring both sides we get 

sin² A + cos² A + 2 sin A cos A = 1

1 + sin 2A = 1 

sin 2A = 0