Question

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

• A. $0$
• B. $\sin x$
• C. $\cos x$
• D. $1$

Answer 1

Answer: (D)

$1$

Given:$\frac{{\sin }^{3}x+{\cos }^{3}x}{\sin x+\cos x}+\sin x\cos x$

$=\frac{(\sin x+\cos x)({\sin }^{2}x-\sin x\cos x+{\cos }^{2}x)}{\sin x+\cos x}+\sin x\cos x$ ......$[\therefore a^3+b^3=(a+b)(a^2-ab+b^2)]$ and

.....$(\because {\sin }^{2}x+{\cos }^{2}x=1)$

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

$=1$