List of top Mathematics Questions on Inverse Trigonometric Functions asked in UP Board XII

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 \(\sin^{-1}\left(\dfrac{1}{\sqrt2}\right)\).

Prove that \(3\cos^{-1}x=\cos^{-1}(4x^3-3x),\ x\in\left[\dfrac12,1\right]\).

Write \(\tan^{-1}\left(\dfrac{x}{\sqrt{a^2-x^2}}\right),\ |x|<a\) in simplest form.

\(\sin(\tan^{-1}x),\ |x|<1\) is equal to:

Simplify: \(\tan^{-1}\!\left(\dfrac{3a^{2}x-x^{3}}{a^{3}-3ax^{2}}\right)\).

If \(\sin^{-1}(1-x)-2\sin^{-1}x=\dfrac{\pi}{2}\), then find the value of \(x\).

Find the value of \(\cos^{-1}\Big(\dfrac12\Big)+2\sin^{-1}\Big(\dfrac12\Big)\).

Write \(\cot^{-1}\!\Big(\dfrac{1}{\sqrt{x^{2}-1}}\Big)\), \(x>1\) in the simplest form.

If \(x\in\left(0,\dfrac{\pi}{4}\right)\), then prove that \(\cot^{-1}\left(\dfrac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}}\right)=\dfrac{x}{2}\).

Find the value of \(\tan^{-1}\sqrt3-\sec^{-1}(-2)\).

\(\sin(\tan^{-1}x)\), \(|x|<1\) is equal to: