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}$