Question

If $\sin x+\cos x=\sqrt{2}$ , then $\sin x\cos x$ =

• A. 1
• B. $\frac{1}{2}$
• C. 2
• D. $\sqrt{2}$
• E. $\frac{1}{\sqrt{2}}$

Answer 1

Answer: (B)

$\sin x+\cos x=\sqrt{2}$
$\Rightarrow (\sin x+\cos x{)}^2=(\sqrt{2}{)}^2$
$\Rightarrow {\sin }^{2}x+{\cos }^{2}x+2\sin x\cos x=2$
$\Rightarrow 1+2\sin x\cos x=2$
$\Rightarrow 2\sin x\cos x=1$
$\Rightarrow \sin x\cos x=\frac{1}{2}$