Question

Rewrite with only sin x and cos x. (1 point)

sin 2x - cos 2x


2 sinx cosx - 1 + 2 sin2x
2 sin x cos2x - 1 + 2 sin2x
2 sin x cos2x - sin x + 1 - 2 sin2x
2 sin x cos2x - 1 - 2 sin2x

Answer 1

Note that
sin 2x = 2 sin(x) cos(x)
cos 2x = cos²x - sin²x = 2cos²x - 1 = 1 - 2sin²x

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

Answer: 2 sin(x) cos(x) - 1 + 2 sin²x