List of top Mathematics Questions on Inverse Trigonometric Functions

The Value of tan⁻¹ [2sin{2cos⁻¹ ($\frac {\sqrt 3}{2}$)}].

If the inverse trigonometric functions take principal values, then
$cos^{-1} ( \frac{3}{10} cos (tan^{-1} (\frac{4}{3})) + \frac{2}{5} sin (tan^{-1} (\frac{4}{3})))$
is equal to :

Let
$f(x)=2cos^{−1}⁡x+4cot^{−1}⁡x−3x^2−2x+10,X∈[−1,1]$
If [a, b] is the range of the function, f then 4a – b is equal to :

$\tan \left(2 \tan ^{-1} \frac{1}{5}+\sec ^{-1} \frac{\sqrt{5}}{2}+2 \tan ^{-1} \frac{1}{8}\right)$ is equal to:

Considering the principal values of the inverse trigonometric functions, the sum of all the solutions of the equation $\cos ^{-1}(x)-2 \sin ^{-1}(x)=\cos ^{-1}(2 x)$ is equal to:

Let $f(x)=\frac{4x+3}{x+2}$, Then the value of $f^{-1}(-2)$ is equal to

$tan(2tan^{-1}(\frac{2}5))$ is equal to

The value of $sin^2(cos^{-1}(\frac{3}5))$ is equal to

The value of $tan^{-1} (\frac{7}4) - tan^{-1} (\frac{3}{11})$ is equal to

$\tan^{-1}[\frac{1}{\sqrt3}\sin\frac{5\pi}{2}]\sin^{-1}[\cos(\sin^{-1}\frac{\sqrt3}{2})]=$

If f(x) = sin^-1$(\frac{2x}{1+x^2})$, then f'$(\sqrt3)$ is

Considering only the principal values of inverse functions, the set $A = \{ x \ge 0 : \tan^{-1} (2x) + \tan^{-1} (3x) = \frac{\pi}{4} \}$

If $\cos^{-1} \frac{3}{5} + \cos^{-1} \frac{12}{13} = \cos^{-1} k$, then the value of $k$ is

The value of $\tan^{-1} \left[\frac{\sqrt{1+x^{2}} + \sqrt{1-x^{2}}}{\sqrt{1+x^{2}} - \sqrt{1-x^{2}}}\right] , \left|x\right| < \frac{1}{2}, x \ne0, $ is equal to :

If $y=\sin^{-1}\frac{1}{2}(\sqrt{1+x}+\sqrt{1-x})$ then y' =

If $tan^{-1} \,x + tan^{-1} \,y = \frac{4\pi}{5}$, then $cot^{-1}\, x + cot^{-1} \,y$ is equal to

If $\sin^{-1} \, x + \sin^{-1} \,y= \frac{\pi}{2}$ , then $x^2$ is equal to

If $ 2 \,tan^{-1} (cos\,x) = tan^{-1} (2 \,cosec\,x)$ then $sin\,x + cos\,x $ is equal to

The simplified form of $\tan^{-1}$ $\left(\frac{x}{y}\right)$ $- \tan^{-1}$ $\left(\frac{x-y}{x+y}\right)$ is equal to

$ \frac{sin\,60^{\circ}+i\,cos\,60^{\circ}}{cos\,15^{\circ}-i\,sin\,15^{\circ}}= $

$\sin^{2}\,\theta\, \cos^{3}\,\theta-\sin^{4}\,\theta\, \cos\,\theta$ is equal

If $f\left(x\right) = 2 \tan^{-1} x + \sin^{-1} \left(\frac{2x}{1+x^{2}}\right), x > 1$, then $f(t)$ is equal to :

$\cot^{-1} (21) + \cot^{-1} (13) + \cot^{-1} (-8) =$

$\tan\left(\cos^{-1}\left( \frac{1}{5\sqrt{2}}\right)-\sin^{-1}\left(\frac{4}{\sqrt{17}}\right)\right)$ is

If $\tan(x + y) = 33$ and $x = \tan^{-1} \, 3,$ then $y$ is

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