SOLUTION: Please can you help with the following question? (sin�+cos�)(1-sin�cos�)=sin^3�+cos^3�

Question 577930: Please can you help with the following question?
(sin�+cos�)(1-sin�cos�)=sin^3�+cos^3�
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
(sin(�)+cos(�))(1-sin(�)cos(�))=sin^3(�)+cos^3(�)

sin(�)-sin^2(�)cos(�)+cos(�)-sin(�)cos^2(�)=sin^3(�)+cos^3(�)

sin(�)-(1-cos^2(�))cos(�)+cos(�)-sin(�)(1-sin^2(�))=sin^3(�)+cos^3(�)

sin(�)-cos(�)+cos^3(�)+cos(�)-sin(�)+sin^3(�)=sin^3(�)+cos^3(�)

(sin(�)-sin(�))+(-cos(�)+cos(�))+(sin^3(�)+cos^3(�))=sin^3(�)+cos^3(�)

sin^3(�)+cos^3(�)=sin^3(�)+cos^3(�)

So this verifies the identity.

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