Question

if $2co{s}^{-1}\sqrt{\frac{1+x}{2}}=\frac{\pi }{2}$, then x=

• A. $1$
• B. $0$
• C. $\frac{-1}{2}$
• D. $\frac{1}{2}$

Answer 1

The correct option is B $0$

Given equation is $2co{s}^{-1}\sqrt{\left(\frac{1+x}{2}\right)}=\frac{\pi }{2}$
$\Rightarrow co{s}^{-1}\sqrt{\left(\frac{1+x}{2}\right)}=\frac{\pi }{4}\Rightarrow cos\frac{\pi }{4}=\frac{\sqrt{1+x}}{\sqrt{2}}$
$\Rightarrow \frac{1}{\sqrt{2}}=\frac{\sqrt{1+x}}{\sqrt{2}}\Rightarrow 1=\sqrt{1+x}\Rightarrow x=0$.