What is the value of \frac{\sin^3x+\cos^3x}{\sin x+\cos x}+\sin x\cos x?

Trigonometry Practice Test 1

Question : 21 of 40

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What is the value of

{\sin^3x+\cos^3x}/{\sin x+\cos x}+\sin x\cos x?

Solution:

{\sin^3x+\cos^3x}/{\sin x+\cos x}+\sin x\cos x

={(\sin x+\cos x)(\sin^2x+\cos^2x-\sin x\cos x)}/{\sin x+\cos x}+\sin x\cos x

=1-\sin x\cos x+\sin x\cos x=1

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