Question

How to solve sinx cosx tanx= 1- cos^2x ?

Answer 1

Please see below.

Explanation:

We know that `tanx=sinx/cosx`

Let's plug it in:

`sinxcosx*sinx/cosx=1-cos^2x`

`sinxcancelcosx*sinx/cancelcosx=1-cos^2x`

`sin^2x=1-cos^2x`

But we know the most famous Trigonometric identity says:

`sin^2x+cos^2x=1`

If we subtract `cos^2x` from both sides, we get:

`sin^2x+cos^2x-cos^2x=1-cos^2x`

`sin^2x=1-cos^2x`

We can plug it in:

`1-cos^2x=1-cos^2x`

You now have the proof.