Write the function in the simplest form: tan | vedclass

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

Question

(D) Given expression: $	an ^{-1} \frac{x}{\sqrt{a^{2}-x^{2}}}$Let $x = a \sin 	heta$. Then $\frac{x}{a} = \sin 	heta$,which implies $	heta = \sin

Vedclass · Accepted Answer

$\sin ^{-1} \frac{x}{a}$

Vedclass · Answer

(D) Given expression: $	an ^{-1} \frac{x}{\sqrt{a^{2}-x^{2}}}$Let $x = a \sin 	heta$. Then $\frac{x}{a} = \sin 	heta$,which implies $	heta = \sin ^{-1} \left(\frac{x}{a}ight)$.Substituting $x = a \sin 	heta$ into the expression:$= 	an ^{-1} \left(\frac{a \sin 	heta}{\sqrt{a^{2} - a^{2} \sin ^{2} 	heta}}ight)$$= 	an ^{-1} \left(\frac{a \sin 	heta}{\sqrt{a^{2}(1 - \sin ^{2} 	heta)}}ight)$$= 	an ^{-1} \left(\frac{a \sin 	heta}{a \cos 	heta}ight)$$= 	an ^{-1} (	an 	heta)$$= 	heta = \sin ^{-1} \left(\frac{x}{a}ight)$

Write the function in the simplest form: $\tan ^{-1} \frac{x}{\sqrt{a^{2}-x^{2}}}, |x| < a$

Similar Questions

Let $\mathop {Lim}\limits_{x \to 0} \sec^{-1} \left( \frac{x}{\sin x} \right) = l$ and $\mathop {Lim}\limits_{x \to 0} \sec^{-1} \left( \frac{x}{\tan x} \right) = m$,then

$\sin^{-1}(\sin \frac{7\pi}{6}) = $

The value of $\tan^{-1} \left( \frac{\cos(\frac{19\pi}{4}) - 1}{\sin(\frac{\pi}{4})} \right)$ is equal to

The real part of $\sin^{-1}(e^{i\theta})$ is

If $\tan ^{-1}\left(\frac{1-x}{1+x}\right)=\frac{1}{2} \tan ^{-1} x$,then $x$ has the value

Vedclass Test Series

Exam Paper Generator

Online Exam Module