SOLUTION: I have been having trouble solving this problem, using trigonometric identities: {{{ 1-2cos^2(x)=sin^4(x)-cos^4(x) }}} I have to prove it is an identity, preferably using the lef

Algebra ->  Trigonometry-basics -> SOLUTION: I have been having trouble solving this problem, using trigonometric identities: {{{ 1-2cos^2(x)=sin^4(x)-cos^4(x) }}} I have to prove it is an identity, preferably using the lef      Log On


   



Question 611721: I have been having trouble solving this problem, using trigonometric identities:
+1-2cos%5E2%28x%29=sin%5E4%28x%29-cos%5E4%28x%29+
I have to prove it is an identity, preferably using the left-hand side.
I would appreciate any help given.
Thank you!

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
identity substitution and factoring (difference of squares)
___ [sin^2(x) + cos^2(x)] - 2 cos^2(x) = [sin^2(x) + cos^2(x)] [sin^2(x) - cos^2(x)]

consolidation of terms and identity substitution ___ sin^2(x) - cos^2(x) = 1 [sin^2(x) - cos^2(x)]