Question

Prove cos^2x tanx / sinx = cosx?

Answer 1

We seek to prove that:

`cos^2x tanx/sinx -= cos x`

Consider the LHS of the expression:

`LHS -= cos^2x tanx/sinx`

`\ \ \ \ \ \ \ \ = cos x * cosx * ((sinx/cosx)) / sin x`

`\ \ \ \ \ \ \ \ = cos x * cosx * (sinx/cosx) * 1/ sin x`

After cancelling we get:

`LHS = cos x * cancel(cosx) * (cancel(sinx)/cancel(cosx)) * 1/ cancel(sin x)`

`\ \ \ \ \ \ \ \ = cos x`

`\ \ \ \ \ \ \ \ = RHS \ \ \ QED`