# How do I proof this equation is an identity? 1-sec(x)cos³(x)=sin²(x)

##### 3 Answers

Recall that

#1 - (1/cosx)cos^3x= sin^2x#

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

And since

#sin^2x= sin^2x#

#LHS = RHS#

Hopefully this helps!

Pythagorean Identity:

And reciprocal identity:

Applied to:

Use these three identities (the third one is pretty much the same as the second, but switched around a little):

To complete the proof, I'll start with the left-hand side of the equation and manipulate it until it equals the right-hand side of the equation:

That is the proof. Hope this helped!