Question

1 + cos20/sin 20= cot 0

Answer 1

To prove the identity we need to remember the following identities:

`\cos ^2\theta+\sin ^2\theta=1`
`\tan \theta=(\sin \theta)/(\cos \theta)`

With this in mind we have:

`\begin{gathered} (\cos^2\theta+\sin^2\theta)/(1+\tan^2\theta)=(1)/(1+(\sin ^2\theta)/(\cos ^2\theta)) \\ =(1)/((\cos ^2\theta+\sin ^2\theta)/(\cos ^2\theta)) \\ =(1)/((1)/(\cos ^2\theta)) \\ =\cos ^2\theta \end{gathered}`

This proves the identity.