Question

Express each of the following in terms of sinθ and/or cosθ.

a) cosθ 1/secθ

b) tanθcosθ

c) 1+cot^2θ/cot^2θ

Answer 1

\(\tan(x)=\frac{\sin(x)}{\cos(x)}\) so second one is
\[\frac{\sin(x)}{\cos(x)}\times \cos(x)=\frac{\sin(x)}{\cancel{\cos(x)}}\times \cancel{\cos(x)}=\sin(x)\]

Answer 2

third one \(1+cot^2(x)=\csc^2(x)\) so you get
\[\frac{\csc^2(x)}{\cot^2(x)}\]
\[=\frac{\frac{1}{\sin^2(x)}}{\frac{\cos^2(x)}{\sin^2(x)}}\]
\[=\frac{1}{\sin^2(x)}\times \frac{\sin^2(x)}{\cos^2(x)}\]
\[=\frac{1}{\cos^2(x)}\]

Answer 3

thanks!

Answer 4

Didn't get the first one