Question

Find the non-zero value of $x$ which satisfies the equation $arc\sin x=arc\cos \left(2x\right)$

• A. $0.866$
• B. $0.707$
• C. $0.500$
• D. $0.447$
• E. $0.245$

Answer 1

The correct option is D $0.447$

Given, $arc\sin x=arc\cos \left(2x\right)$

Let it be equal to $\theta$.
We get $x=\sin \theta$ and $2x=\cos \theta$ , which implies $2\sin \theta =\cos \theta$
By squaring it on both sides, we get

$4{\sin }^{2}x={\cos }^{2}x=1-{\sin }^{2}x$
Which implies $\sin x=\frac{1}{\sqrt{5}}=0.447$