Question

Reposting because I really need help!

Rewrite using only cos and sin: cos 2x - sin x
Answer choices:
A) cos^2x - sin^2x - sin x
B) cos^2x - sin^3x
C) cos^2x + sin^2x + sin x
D) cos^2x - 3 sin x

Answer 1

we use the same double angle identity.


`\bf \textit{Double Angle Identities} \\ \quad \\ sin(2\theta)=2sin(\theta)cos(\theta) \\ \quad \\\\ cos(2\theta)= \begin{cases} \boxed{cos^2(\theta)-sin^2(\theta)}\\ 1-2sin^2(\theta)\\ 2cos^2(\theta)-1 \end{cases} \\ \quad \\\\ tan(2\theta)=\cfrac{2tan(\theta)}{1-tan^2(\theta)}\\\\ -------------------------------\\\\ cos(2x)-sin(x)\implies \boxed{cos^2(x)-sin^2(x)}-sin(x)`