Rewrite with only sin x and cos x.

1.) sin 2x - cos x

A.)2 sin x cos2x

B.)sin x

C.)cos x (2 sin x - 1)

D.)2 sin x

Question#2
Rewrite with only sin x and cos x.

sin 2x - cos 2x

A.) 2 sin^2x cos x - 1 + 2 sin^2x

B.) 2 sin x cos^2x - 1 + 2 sin^2x

C.) 2 sin x cos^2x - sin x + 1 - 2 sin^2x

D.) 2 sin x cos^2x - 1 - 2 sin^2x

1. C

sin(2x) - cos(x)
= 2 sin(x) cos(x) - cos(x)
= cos(x) (2 sin(x) - 1)

2.

sin(2x) - cos(2x)
= 2 sin(x) cos(x) − (1 − 2sin²x)
= 2 sin(x) cos(x) − 1 + 2sin²x

Doesn't seem to match any of the answers given

1.
sin(2x) - cos(x)
= 2sin(x)cos(x) - cos(x)
=cos(x)(2sin(x) - 1)

2.
sin(2x) - cos(2x)
=2sin(x)cos(x) - cos^2(x) + sin^2(x)
but cos^2(x) = 1 - sin^2(x)
so = 2sin(x)cos(x) - 1 + 2sin^2(x)