List of top Mathematics Questions on Inverse Trigonometric Functions

If \[ \tan^{-1}\left(\frac{1}{2\sqrt2}\right) - \cos^{-1}\left(\frac{1}{\sqrt3}\right) + \sin^{-1}(x) = 0, \] then \(x=\)

Evaluate \[ \tan^{-1}\left(\frac12\right) +\tan^{-1}\left(\frac18\right) +\tan^{-1}\left(\frac1{18}\right) +\tan^{-1}\left(\frac1{32}\right). \]

If \[ (2\sin^{-1}x)^3=\pi^3-(2\cos^{-1}x)^3 \] then one value of \[ \cos(2\sin^{-1}x-3\cos^{-1}x) \] is

If \(x\in\left(0,\frac{1}{\sqrt2}\right)\), then \[ \cot\left[\cos^{-1}\{\tan(\sin^{-1}x)\}\right]= \]

If \(a_1,a_2,a_3,\ldots ,a_n\) are in arithmetic progression with common difference d, then \(tan[tan^{-1}(\frac{d}{1+a_1a_2})+tan^{-1}(\frac{d}{1+a_2a_3})+\ldots +tan^{-1}(\frac{d}{1+a_{n-1}a_n})] =\) ____

The value of \(sin^{-1}(sin\frac{5π}{6})+cos^{-1}(cos\frac{7π}{6})+tan^{-1}(tan\frac{2π}{3})\) is equal to...

If \(sin^{-1}(tan\frac{π}{4})-sin^{-1}(\sqrt{\frac{3}{x}}) = \frac{π}{6}\) then \(x\) is a root of the equation

\(\sum _{k = 1}^{2026}sin^{-1}(cos\frac{kπ}{4}) =\)

For \(x > 0\), if \(sin(cos^{-1}x+tan^{-1}x)-cos(sin^{-1}x+tan^{-1}x) = sin(cot^{-1}2)\) then \(x =\)

If \(0\leq x\leq 1\), \(I_1 = \int sin^{-1}\sqrt{1-x^2}\,dx\) and \(I_2 = \int sin^{-1}x\,dx\), then which of the following is true?

If \((tan^{-1}x)^2+(cot^{-1}x)^2 = \frac{5π^2}{8}\), then the value of \(x\) is equal to...

\(cos(cos^{-1}(-\frac{1}{2})+\frac{π}{3}) =\)

If \(y = tan^{-1}[\frac{x-\sqrt{1-x^2}}{x+\sqrt{1-x^2}}]\) , then \(\frac{dy}{dx} =\)

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

If \(y = tan^{-1}(\frac{1}{x^2+x+1})+tan^{-1}(\frac{1}{x^2+3x+3})+tan^{-1}(\frac{1}{x^2+5x+7})+\ldots\) upto \(n\) terms, then \(y^'(0) =\)

If \(cot(cos^{-1}x) = sec(tan^{-1}\frac{a}{\sqrt{b^2-a^2}})\), then the value of \(x\) is

The minimum value of \((sin^{-1}x)^2+(cos^{-1}x)^2\) is............

The value of \(tan^{-1}(\sqrt{3})+sec^{-1}(-2)-sin^{-1}(-\frac{1}{2})\) is

Write \(\tan^{-1}\left(\dfrac{\cos x-\sin x}{\cos x+\sin x}\right)\), \(\dfrac{-\pi}{4}<x<\dfrac{3\pi}{4}\) in the simplest form.

The value of \(\tan^{-1}(\sqrt{3}) - \cot^{-1}(-\sqrt{3})\) is:

Show that \(\sin^{-1}\dfrac{12}{13}+\cos^{-1}\dfrac{4}{5}+\tan^{-1}\dfrac{63}{16}=\pi\).

Show that \(\tan^{-1}\dfrac{2}{11}+\tan^{-1}\dfrac{7}{24}=\tan^{-1}\dfrac{1}{2}\).

The value of \(\cos(\sec^{-1}x+\text{cosec}^{-1}x)\), \(|x|\ge 1\) is

Prove that \(\tan^{-1}\dfrac15+\tan^{-1}\dfrac17+\tan^{-1}\dfrac13+\tan^{-1}\dfrac18=\dfrac\pi4\).

Find the principal value of \(\sin^{-1}\left(\dfrac{1}{\sqrt2}\right)\).