If $\sec^{-1} x = \operatorname{cosec}^{-1} y$, show that $\frac{1}{x^2} + \frac{1}{y^2} = 1$
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Inverse Trigonometric Functions - ISC Class 12 Mathematics Questions with Answers, Page 3
49 past-paper questions on Inverse Trigonometric Functions from ISC Class 12 Mathematics papers (2027-2017), newest first, in full. Questions 41-49 are on this page, 20 to a page. Tap "Show answer" under a question to see its answer.
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Solve for $x$:
$\tan^{-1}\left(\frac{x - 1}{x - 2}\right) + \tan^{-1}\left(\frac{x + 1}{x + 2}\right) = \frac{\pi}{4}$
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Solve: $\sin(2\tan^{-1}x) = 1$
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Prove that $\tan^{-1}\left(\frac{1}{2}\right) = \frac{\pi}{4} - \frac{1}{2} \cos^{-1}\left(\frac{4}{5}\right)$.
Given: $\frac{\pi}{4} - \frac{1}{2} \cos^{-1}\left(\frac{4}{5}\right)$
To show: $\tan^{-1}\left(\frac{1}{2}\right) = \frac{\pi}{4} - \frac{1}{2} \cos^{-1}\left(\frac{4}{5}\right)$
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Solve: $3\tan^{-1}x + \cot^{-1}x = \pi$
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If $\tan^{-1}a + \tan^{-1}b + \tan^{-1}c = \pi$, prove that $a + b + c = abc$.
Given: $\tan^{-1}a + \tan^{-1}b + \tan^{-1}c = \pi$
To show: $a + b + c = abc$
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Solve: $\sin^{-1}(\cos(\sin^{-1} x)) = \frac{\pi}{3}$
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Prove that $\frac{1}{2}\cos^{-1}\left(\frac{1-x}{1+x}\right) = \tan^{-1}\sqrt{x}$.
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Solve the equation for $x$:
$\sin^{-1} x + \sin^{-1}(1 - x) = \cos^{-1} x, \quad x \neq 0$
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