List of top Mathematics Questions on Properties of Inverse Trigonometric Functions asked in MHT CET

If \(3sin^{-1}(\frac{2x}{1+x^2})-4cos^{-1}(\frac{1-x^2}{1+x^2})+2tan^{-1}(\frac{2x}{1-x^2}) = \frac{π}{3}\) then \(x = ?\)

If \(2sin^{-1}x-3cos^{-1}x = 4\), then \(2sin^{-1}x+3cos^{-1}x =\)

If \(tan^{-1}ax+tan^{-1}3x = \frac{π}{4}\), where \(3ax^2 < 1\), then value of \(a\) for \(x = \frac{1}{6}\) is \(\ldots\)

\(sec^2(tan^{-1}3)-tan^2(sec^{-1}3) =\)

If \(0\leq x\leq 1\) and \((sin^{-1}x)^3+(cos^{-1}x)^3 = aπ^3\) then

If \(\sum _{n = 1}^{2026}tan^{-1}(\frac{1}{n^2+n+1}) = tan^{-1}(1-\frac{1}{x})\), where \(x\neq 0\), then \(x =\)

If \(y = \frac{1}{3x+5}\), then the value of \(\frac{d^9y}{dx^9}\) is..

The value of \(3tan^{-1}(\frac{1}{2}) = \ldots\)

The value of \(cot^{-1}[\frac{\sqrt{1-sinx}+\sqrt{1+sinx}}{\sqrt{1-sinx}-\sqrt{1+sinx}}]\), where \(x\in (0,\frac{π}{2})\) is...

\(sin^{-1}(\frac{12}{13})+cos^{-1}(\frac{4}{5})+tan^{-1}(\frac{63}{16}) =\)

If \(tan^{-1}[\frac{\sqrt{5-2\sqrt{6}}}{1+\sqrt{6}}] = \frac{π}{3}-tan^{-1}(k)\), then \(sec^{-1}(k) = ...\)

Let \(f(x) = (sin^{-1}x)^2+(cos^{-1}x)^2\) be a real-valued function defined on its domain. Then the sum of the greatest and the least values of \(f(x)\) is

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

If \(tan^{-1}(1)+tan^{-1}(3)+tan^{-1}(5)+tan^{-1}(\frac{1}{4}) = π+tan^{-1}(\frac{α}{2})\), then the value of \(α\) is...

Considering only principal values, the value of $\tan(\sin^{-1}(\frac{3}{5})-2 \cos^{-1}(\frac{2}{\sqrt{5}}))$ is}

If $y = \operatorname{cosec}^{-1} \left[ \frac{\sqrt{x}+1}{\sqrt{x}-1} \right] + \cos^{-1} \left[ \frac{\sqrt{x}-1}{\sqrt{x}+1} \right]$, then $\frac{dy}{dx} =$

$\tan ^{-1}\left(\frac{x-1}{x-2}\right)+\tan ^{-1}\left(\frac{x+1}{x+2}\right)=\frac{\pi}{4}$, then the values of $x$ are