Question

Can you prove `1- \cos ^ { 2} x = \sin x \cos x \tan x`?

Answer 1

See below

Explanation:

Recall that `tanx=sinx/cosx` and the Pythagorean identity `sin^2x+cos^2x=1`

From the identity it can be determined that `sin^2x=1-cos^2x`

`sinxcosxtanx=sinxcosx(sinx/cosx)=sinxsinx=sin^2x=1-cos^2x`

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

`"Q.E.D."`