If 2cos^{-1}sqrt{frac{1+x}{2}} = frac{pi}{2}, | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given equation is $2\cos^{-1}\sqrt{\frac{1+x}{2}} = \frac{\pi}{2}.$Dividing both sides by $2,$ we get $\cos^{-1}\sqrt{\frac{1+x}{2}} = \frac{\pi}{

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(B) Given equation is $2\cos^{-1}\sqrt{\frac{1+x}{2}} = \frac{\pi}{2}.$Dividing both sides by $2,$ we get $\cos^{-1}\sqrt{\frac{1+x}{2}} = \frac{\pi}{4}.$Taking cosine on both sides,we have $\sqrt{\frac{1+x}{2}} = \cos\left(\frac{\pi}{4}\right).$Since $\cos\left(\frac{\pi}{4}\right) = \frac{1}{\sqrt{2}},$ we get $\sqrt{\frac{1+x}{2}} = \frac{1}{\sqrt{2}}.$Squaring both sides,$\frac{1+x}{2} = \frac{1}{2}.$Multiplying by $2,$ we get $1+x = 1,$which implies $x = 0.$

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

Similar Questions

Find the principal value of $\cos ^{-1}\left(-\frac{1}{\sqrt{2}}\right)$.

Find the value of $\cos ^{-1}\left(\cos \frac{7 \pi}{6}\right)$.

$\tan \left[ \sec^{-1} \sqrt{1 + x^2} \right] = $

Write the function in the simplest form: $\tan ^{-1} \frac{x}{\sqrt{a^{2}-x^{2}}}, |x| < a$

Find the principal value of $\sin ^{-1}\left(\frac{1}{\sqrt{2}}\right)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module