Verify the identity: (sinx + tanx + tan^3x)/tanx = cosx + sec^2x

Question

Verify identities showing steps

 

Answer 1

We know that sec^2x-tan^2x = 1

cotx = 1/tanx

Left hand side

= (sinx+tanx+tan^3x)/tanx

= sinx/tanx+tanx/tanx+tan^3x/tanx

= cotxsinx+1+tan^2x

= (cosx/sinx)sinx+sec^2x

= cosx+sec^2x

= Right hand side