Question

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

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

Answer 1

The correct option is B

$0$

Explanation for the correct options:

Finding the value:

Given Data,

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

$\Rightarrow$ ${\cos }^{-1}\sqrt{\frac{1+x}{2}}=\frac{\pi }{4}$

$\Rightarrow$ $\sqrt{\frac{1+x}{2}}=\cos \frac{\pi }{4}$

$\Rightarrow$ $\sqrt{\frac{1+x}{2}}=\frac{1}{\sqrt{2}}$

$\Rightarrow$ $\sqrt{1+x}=1$

$\therefore$ $x=0$

Hence, Option (B) is correct.