Question

Prove that:
cosx(tanx+cotx)=cscx

Answer 1

\[LHS=cosx(\frac{sinx}{cosx}+\frac{cosx}{sinx})=cosx(\frac{\sin^2x+\cos^2x}{sinxcosx})\]
\[=cosx(\frac{1}{sinxcosx})\]
\[=\cancel{cosx}(\frac{1}{sinx \cancel{cosx}})\]
\[=\frac{1}{sinx}=cosecx=RHS\]

Answer 2

awesome!