Question

Find the principal solution of $\sqrt{\frac{1+2sinx}{2}}=1$

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

Answer 1

The correct option is A

$x=\frac{\pi }{6}$

$\sqrt{\frac{1+2sinx}{2}}=1$
Squaring, we get
$\frac{1+2sinx}{2}=11+2sinx=22sinx=1sinx=\frac{1}{2}x=\frac{\pi }{6}$