Given:
[tex]\cos x\cdot\csc x[/tex]
Express in terms of sine and cosines.
[tex]\cos x\cdot\csc x=\cos x\cdot\frac{1}{\sin x}[/tex]
We know that
[tex]\text{A quotient identity }\cot x=\frac{\cos x}{\sin x}\text{.}[/tex]
Apply a quotient identity.
[tex]\cos x\cdot\csc x=\cot x[/tex]
Hence proved
[tex]\cos x\cdot\csc x=\cot x[/tex]
