If y = tan^{-1}left( frac{acos x - bsin x}{bc | vedclass

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

Question

(B) Given $y = 	an^{-1}\left( \frac{a\cos x - b\sin x}{b\cos x + a\sin x} ight)$.Divide the numerator and denominator by $b\cos x$:$y = 	an^{-1}\l

Vedclass · Accepted Answer

$-1$

Vedclass · Answer

(B) Given $y = 	an^{-1}\left( \frac{a\cos x - b\sin x}{b\cos x + a\sin x} ight)$.Divide the numerator and denominator by $b\cos x$:$y = 	an^{-1}\left( \frac{\frac{a}{b} - 	an x}{1 + \frac{a}{b}	an x} ight)$.Let $\frac{a}{b} = 	an 	heta$,then $y = 	an^{-1}\left( \frac{	an 	heta - 	an x}{1 + 	an 	heta 	an x} ight)$.Using the formula $	an(A - B) = \frac{	an A - 	an B}{1 + 	an A 	an B}$,we get:$y = 	an^{-1}(	an(	heta - x)) = 	heta - x$.Since $	heta = 	an^{-1}(\frac{a}{b})$ is a constant,differentiating with respect to $x$:$\frac{dy}{dx} = \frac{d}{dx}(	an^{-1}(\frac{a}{b}) - x) = 0 - 1 = -1$.

If $y = \tan^{-1}\left( \frac{a\cos x - b\sin x}{b\cos x + a\sin x} \right)$,then $\frac{dy}{dx} = $

Similar Questions

Differentiation of $\tan ^{-1}\left(\frac{x}{\sqrt{1-x^2}}\right)$ with respect to $\sin ^{-1}\left(3 x-4 x^3\right)$ is $....$

If $y = \tan^{-1} \left[ \frac{5 \cos x - 12 \sin x}{12 \cos x + 5 \sin x} \right]$, then $\frac{dy}{dx}$ is equal to

If $y=\sin ^2\left(\cot ^{-1} \sqrt{\frac{1+x}{1-x}}\right)$,then $\frac{d y}{d x}$ has the value

Find the derivative of $\cos^{-1}\sqrt{\cos x}$ with respect to $x$.

If $y(x)=\tan ^{-1}\left(\frac{\sqrt{1+a^2 x^2}-1}{a x}\right)$ and $\left(1+a^2 x^2\right) y^{\prime \prime}+g(x) y^{\prime}=0$, then the sum of the roots of the equation $1+a^2 x^2+g(x)=0$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module