Question

Rewrite with only sin x and cos x. sin 2x - cos x

Answer 1

`\bf sin(2\theta)=2sin(\theta)cos(\theta)\\\\ -------------------------------\\\\ sin(2x)-cos(x)\implies 2sin(x)cos(x)-cos(x) \\\\\\ cos(x)[2sin(x)-1]`

Answer 2

cos(x)(2sinx -1 )

Explanation:

sin 2x - cos x

WE use sin(2x) identity

sin(2x)= 2sin(x)cos(x)

now we plug in our given expression

sin 2x - cos x

2sin(x)cos(x)- cos(x)

we factor out cos(x)

when we factor out cos(x), divide each term by cos(x)

cos(x)(2sinx -1 )

we got the final answer in terms of sinx and cosx