The 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

(D) We are given the equation: $\sin(\cot^{-1}(1 + x)) = \cos(	an^{-1} x)$.First,simplify the right-hand side: Let $	an^{-1} x = 	heta$,then $x = \

Vedclass · Accepted Answer

$-\frac{1}{2}$

Vedclass · Answer

(D) We are given the equation: $\sin(\cot^{-1}(1 + x)) = \cos(	an^{-1} x)$.First,simplify the right-hand side: Let $	an^{-1} x = 	heta$,then $x = 	an 	heta$. Since $\cos 	heta = \frac{1}{\sec 	heta} = \frac{1}{\sqrt{1 + 	an^2 	heta}}$,we have $\cos(	an^{-1} x) = \frac{1}{\sqrt{1 + x^2}}$.Next,simplify the left-hand side: Let $\cot^{-1}(1 + x) = \phi$,then $1 + x = \cot \phi$. Since $\sin \phi = \frac{1}{\csc \phi} = \frac{1}{\sqrt{1 + \cot^2 \phi}}$,we have $\sin(\cot^{-1}(1 + x)) = \frac{1}{\sqrt{1 + (1 + x)^2}}$.Equating both sides: $\frac{1}{\sqrt{1 + (1 + x)^2}} = \frac{1}{\sqrt{1 + x^2}}$.Squaring both sides: $1 + (1 + x)^2 = 1 + x^2$.$(1 + x)^2 = x^2$.$1 + 2x + x^2 = x^2$.$1 + 2x = 0$.$x = -\frac{1}{2}$.

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

Similar Questions

The greatest and the least value of ${(\sin ^{ - 1}}x)^3 + {(\cos ^{ - 1}}x)^3$ are

If $\theta = \sec^{-1}(\cosh u)$,then $u =$

The value of $\tan \left(2 \tan ^{-1}\left(\frac{\sqrt{5}-1}{2}\right)\right)$ is

Prove $\tan ^{-1}\left(\frac{\sqrt{1+x}-\sqrt{1-x}}{\sqrt{1+x}+\sqrt{1-x}}\right)=\frac{\pi}{4}-\frac{1}{2} \cos ^{-1} x$,where $-\frac{1}{\sqrt{2}} \leq x \leq 1$.

If $\operatorname{Tan}^{-1} \frac{1}{3}+\operatorname{Tan}^{-1} \frac{1}{7}+\operatorname{Tan}^{-1} \frac{1}{13}+\ldots+\operatorname{Tan}^{-1} \frac{1}{n^2+n+1}=\operatorname{Tan}^{-1} \theta$,then $\theta=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module