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

Algebra ->  Trigonometry-basics -> SOLUTION: Please can you help with the following question? (sinØ+cosØ)(1-sinØcosØ)=sin^3Ø+cos^3Ø      Log On


   

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

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

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

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

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

sin^3(Ø)+cos^3(Ø)=sin^3(Ø)+cos^3(Ø)


So this verifies the identity.