A value of x for which sin(cot^{-1}(1 + x)) = | vedclass

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

Question

(A) Given the equation: $\sin(\cot^{-1}(1 + x)) = \cos(	an^{-1}x)$.Let $	heta = \cot^{-1}(1 + x)$,then $\cot 	heta = 1 + x$. Since $\sin 	heta = \

Vedclass · Accepted Answer

$-\frac{1}{2}$

Vedclass · Answer

(A) Given the equation: $\sin(\cot^{-1}(1 + x)) = \cos(	an^{-1}x)$.Let $	heta = \cot^{-1}(1 + x)$,then $\cot 	heta = 1 + x$. Since $\sin 	heta = \frac{1}{\sqrt{1 + \cot^2 	heta}}$,we have $\sin(\cot^{-1}(1 + x)) = \frac{1}{\sqrt{1 + (1 + x)^2}}$.Let $\phi = 	an^{-1}x$,then $	an \phi = x$. Since $\cos \phi = \frac{1}{\sqrt{1 + 	an^2 \phi}}$,we have $\cos(	an^{-1}x) = \frac{1}{\sqrt{1 + x^2}}$.Equating the two sides: $\frac{1}{\sqrt{1 + (1 + x)^2}} = \frac{1}{\sqrt{1 + x^2}}$.Squaring both sides: $1 + (1 + x)^2 = 1 + x^2$.$1 + 1 + 2x + x^2 = 1 + x^2$.$2 + 2x = 1$.$2x = -1$.$x = -\frac{1}{2}$.

$A$ value of $x$ for which $\sin(\cot^{-1}(1 + x)) = \cos(\tan^{-1}x)$ is

Similar Questions

If $\frac{\pi}{2} \le x \le \frac{3\pi}{2},$ then $\sin^{-1}(\sin x)$ is equal to

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

The value of $\cos^{-1}(\cos \frac{5\pi}{3}) + \sin^{-1}(\sin \frac{5\pi}{3})$ is

If $\cos ^{-1} x = \sin ^{-1}(3x)$,then $x$ is equal to

Considering only the principal values of an inverse function,the set $A = \{x \geq 0 \mid \tan^{-1} x + \tan^{-1} 6x = \frac{\pi}{4}\}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module