SOLUTION: Verify that the following is an identity? (sin^4x-cos^4x) / (sin^3x+cos^3x) = (sinx-cosx) / (1-sinxcosx) I have no idea how to start..

Algebra ->  Trigonometry-basics -> SOLUTION: Verify that the following is an identity? (sin^4x-cos^4x) / (sin^3x+cos^3x) = (sinx-cosx) / (1-sinxcosx) I have no idea how to start..      Log On


   

Question 912755: Verify that the following is an identity?
(sin^4x-cos^4x) / (sin^3x+cos^3x) = (sinx-cosx) / (1-sinxcosx)
I have no idea how to start..
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Verify that the following is an identity?
(sin^4x-cos^4x) / (sin^3x+cos^3x) = (sinx-cosx) / (1-sinxcosx)
***
start with left side:
%28sin%5E4%28x%29-cos%5E4%28x%29%29%2F%28sin%5E3%28x%29%2Bcos%5E3%28x%29%29


%28sin%28x%29-cos%28x%29%29%2F%281-sin%28x%29cos%28x%29%29
verified: left side=right side
note:
sin%5E4%28x%29-cos%5E4%28x%29 (difference of 2 squares)
sin%5E3%28x%29%2Bcos%5E3%28x%29 (sum of 2 cubes)
sin%5E2%28x%29%2Bcos%5E2%28x%29=1