how can you prove: 1/cot^2x+secxcosx=sec^2x

Question

Using identities, how can I prove this?

Answer 1

We know that 1/cotx = tanx

cosx = 1/secx

left hand side = 1/cot^2x +secxcosx

= tan^2x+1/cosx*cosx

= tan^2x+1

= sec^2x

= Right hand side