Question

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

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

Answer 1

Answer: (B)

$\frac{1}{2}$

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