How can I demonstrate that (sin(T)+cos(T))(1-sin(T)cos(T))=(sin(T))^3+(cos(T))^3
You first develop the expression on the left side of the equation:(sin(T)+cos(T))(1-sin(T)cos(T))=sin(T)-sin^2(T)cos(T)+cos(T)-sin(T)cos^2(T)=sin(T)(1-cos^2(T))+cos(T)(1-sin^2(T))Now, you will need to use the formula cos^2(T)+sin^2(T)=1Hence, 1-cos^2(T)=sin^2(T) and 1-sin^2(T)=cos^2(T)You now have the following equation: (sin(T)+cos(T))(1-sin(T)cos(T))=sin(T)(sin^2(T))+cos(T)(cos^2(T))QED
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