Cosx-1=sinx

Question

verify the trig identity plz help!!!

Answer 1

Hi Sarah. Here's a solution.

cos x - 1 = sin x

cos x - sin x = 1 [rearranging to get the trig functions on the same side

(cos x - sin x)² = 1² [ squaring both sides

cos²x -2 sin x cos x + sin²x = 1

1 - 2 sin x cos x =1 [since sin²x + cos²x = 1

2 sin x cos x = 0

sin 2x = 0

=> 2x = 0 + kπ for k = 0, +-1, +-2, +-3, . . . .

x = kπ/2 for k = 0, +-1, +-2, +-3, . . . .