If 4 sin ^{-1} x + cos ^{-1} x = pi,then x = | vedclass

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

Question

(C) We are given the equation $4 \sin ^{-1} x + \cos ^{-1} x = \pi$. We know the identity $\sin ^{-1} x + \cos ^{-1} x = \frac{\pi}{2}$,which implies

Vedclass · Accepted Answer

$\frac{1}{2}$

Vedclass · Answer

(C) We are given the equation $4 \sin ^{-1} x + \cos ^{-1} x = \pi$. We know the identity $\sin ^{-1} x + \cos ^{-1} x = \frac{\pi}{2}$,which implies $\cos ^{-1} x = \frac{\pi}{2} - \sin ^{-1} x$. Substituting this into the given equation: $4 \sin ^{-1} x + (\frac{\pi}{2} - \sin ^{-1} x) = \pi$ $3 \sin ^{-1} x + \frac{\pi}{2} = \pi$ $3 \sin ^{-1} x = \frac{\pi}{2}$ $\sin ^{-1} x = \frac{\pi}{6}$ Taking the sine of both sides: $x = \sin(\frac{\pi}{6}) = \frac{1}{2}$. Thus,the correct option is $C$.

If $4 \sin ^{-1} x + \cos ^{-1} x = \pi$,then $x = $

Similar Questions

If $y = \cot^{-1} \left( \frac{1 + \sin 5x}{\cos 5x} \right)$, then the value of $\frac{dy}{dx}$ is

If $\sin ^{-1} x - \cos ^{-1} x = \frac{\pi}{6}$, then $x$ is equal to

If $\cos^{-1}\left(\frac{x}{a}\right) + \cos^{-1}\left(\frac{y}{b}\right) = \alpha$,then $\frac{x^2}{a^2} - \frac{2xy}{ab}\cos \alpha + \frac{y^2}{b^2} = $

If $y = \sin^{-1} \left( \frac{5x + 12\sqrt{1-x^2}}{13} \right)$,then $\frac{dy}{dx} = $

If $0 < x < 1$ and $\tan ^{-1}(1-x), \tan ^{-1} x$ and $\tan ^{-1}(1+x)$ are in $A$.$P$.,then $x^3$ is equal to : . . . . . . .

Vedclass Test Series

Exam Paper Generator

Online Exam Module