Question

Simplify sin q + cosq cotq.

Answer 1

D

Explanation:

trust

Answer 2

`\sin q+\cos q\cot q=\sin q+\cos q\cdot(\cos q)/(\sin q)=\sin q+(\cos^2q)/(\sin q)\\\\=(sin^2q)/(\sin q)+(\cos^2q)/(\sin q)=(\sin^2q+\cos^2q)/(\sin q)=(1)/(\sin q)=\csc q\\\\Used:\\\cot q=(\cos q)/(\sin q)\\\\\sin^2q+\cos^2q=1\\\\\csc q=(1)/(\sin q)`