Question

write the following term of sin(theta) and cos(theta) then simplify.
sec(theta)-tan(theta)sin(theta)

Answer 1

We start as such:
\[
\sec(\theta)-\frac{\sin(\theta)}{\cos(\theta)}\sin(\theta)=\sec(\theta)-\frac{\sin^2(\theta)}{\cos(\theta)}=\\
\frac{1}{\cos(\theta)}-\frac{\sin^2(\theta)}{\cos(\theta)}=\frac{1-\sin^2(\theta)}{\cos(\theta)}=\frac{\cos^2(\theta)}{\cos(\theta)}=\cos(\theta)
\]

Answer 2

thanks a ton LolWolf..<3

Answer 3

Sure thing

Answer 4

Oh, I don't know if it is required, but don't forget the restrictions:\[x\ne \frac{k\pi}{2}, k\in\mathbb{Z}\]