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^2x1−(1cosx)cos3x=sin2x
1 - cos^2x = sin^2x1−cos2x=sin2x
And since
sin^2x= sin^2xsin2x=sin2x
LHS = RHSLHS=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!