Question

The function $\sin \, x + \cos \, x$ is maximum when $x$ is equal to

• A. $\frac{\pi}{6}$
• B. $\frac{\pi}{4}$
• C. $\frac{\pi}{3}$
• D. $\frac{\pi}{2}$

Answer 1

Answer: (B)

$\frac{\pi}{4}$

Answer 2

Let $y=\sin x+\cos x$
$=\sqrt{2}\left(\frac{\sin x+\cos x}{\sqrt{2}}\right)$
$=\sqrt{2}\left(\sin \left(\frac{\pi}{4}+x\right)\right)$
Here, $y$ will be maximum when $\left(\sin \left(\frac{\pi}{4}+x\right)\right)=1$
But, $\sin \frac{\pi}{2}=1$
So, $\frac{\pi}{4}+x=\frac{\pi}{2}$
Hence, $x=\frac{\pi}{4}$