Inverse Trigonometric Functions - ISC Class 12 Mathematics Questions with Answers
49 past-paper questions on Inverse Trigonometric Functions from ISC Class 12 Mathematics papers (2027-2017), newest first. Open one to see its answer.
- Parag is working on a school project on right-angled triangles. He draws a right-angled triangle PQR with $\angle R = 90^\circ$… 2027 · 2 marks · Short answer
- The equation given below has equal roots: $ax^2 + \sin^{-1}(x^2 - 2x + 2) + \cos^{-1}(x^2 - 2x + 2) = 0$ What is the value of… 2027 · 2 marks · Short answer
- If $\theta = \sin^{-1}x + \cos^{-1}x - \tan^{-1}x$, $x \ge 0$, then the smallest interval in which $\theta$ lies is: 2027 · 1 mark · MCQ
- Solve: $\sin^{-1}(x) + \sin^{-1}(1-x) = \cos^{-1} x$. (Application) 2026 · 4 marks · Short answer
- If $\tan^{-1}\left(\frac{\sqrt{1+x^2} - \sqrt{1-x^2}}{\sqrt{1+x^2} + \sqrt{1-x^2}}\right) = \alpha$, prove that… 2026 · 4 marks · Derivation
- Find the principal value of $\sec^{-1}(-\sqrt{2})$. 2026 · 1 mark · Short answer
- Statement 1: If $0 < x < \frac{\pi}{2}$ then the value of $\tan^{-1}(\cot x) = \frac{\pi}{2} - x$ Statement 2… 2026 · 1 mark · MCQ
- If $\cos^{-1} x + \cos^{-1} y + \cos^{-1} z = \pi$, then find the value of $x^2 + y^2 + z^2 + 2xyz$. 2026 · 4 marks · Numerical
- Solve for $x$: $2\tan^{-1}\left(\frac{1}{3}\right) + \sec^{-1}\left(\frac{5\sqrt{2}}{7}\right) = \tan^{-1} x$ 2026 · 4 marks · Short answer
- A music streaming app uses the function: $f(x) = \tan^{-1}\left(\frac{x}{10}\right)$ to assign a mood score based on the number… 2026 · 2 marks · Numerical
- If $\tan^{-1} x + \tan^{-1} y = \frac{\pi}{4}$, then $x + y + xy = 1$. Which one of the following is correct? 2026 · 1 mark · Assertion-reason
- If $\tan^{-1} 2x + \tan^{-1} 3x = \frac{\pi}{4}$, then: Prove that $6x^2 + 5x - 1 = 0$. Hence, solve the equation… 2026 · 4 marks · Short answer
- The equation $\sin^{-1} x - \cos^{-1} x = \cos^{-1}\left(\frac{\sqrt{3}}{2}\right)$ has: 2026 · 1 mark · MCQ
- If $a + \frac{\pi}{2} < 2\tan^{-1} x + 3\cot^{-1} x < b$, then $a$ and $b$ are respectively: 2025 · 1 mark · MCQ
- Find the value of: $\tan^{-1} \left(\frac{x}{y}\right) + \tan^{-1} \left(\frac{y-x}{y+x}\right)$ [Application] 2025 · 2 marks · Short answer
- If $\cos^{-1}\frac{x}{a} - \cos^{-1}\frac{y}{b} = \frac{\pi}{3}$ and… 2025 · 1 mark · Short answer
- Which one of the following is true? 2025 · 1 mark · MCQ
- If the domain of the function $f(x) = \sqrt{\cos^{-1}(3x) + \frac{\pi}{4}}$ is $[a, b]$, then find the value of $a+b$. 2025 · 1 mark · Short answer
- Solve the equation: $\tan^{-1}\left(\frac{x-1}{x-2}\right) + \tan^{-1}\left(\frac{x+1}{x+2}\right) = \frac{\pi}{4}$ 2025 · 2 marks · Short answer
- Find the value of: $\cot \left[\sum_{n=1}^{25} \cot^{-1} \left(1 + \sum_{k=1}^n 2k\right)\right]$. 2025 · 4 marks · Short answer
- Observe the two graphs, Graph 1 and Graph 2 given below and answer the questions that follow. Which one of the graphs represents… 2025 · 6 marks · Short answer
- Solve: $\sin^{-1}(x) + \sin^{-1}(1-x) = \cos^{-1} x$. [Application] 2025 · 4 marks · Short answer
- Find the value of $\tan^{-1} x - \cot^{-1} x$, if $(\tan^{-1} x)^2 - (\cot^{-1} x)^2 = \frac{5\pi^2}{8}$ 2025 · 2 marks · Short answer
- Consider the function $y = \sin^{-1}(2x\sqrt{1 - x^2}), x \in \left[-\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right]$ Find the… 2025 · 6 marks · Short answer
- If… 2025 · 2 marks · Short answer
- Solve for $x$: $\sin^{-1}\left(\frac{x}{2}\right) + \cos^{-1} x = \frac{\pi}{6}$ 2024 · 4 marks · Numerical
- The value of… 2024 · 1 mark · MCQ
- If $\sin^{-1} x + \sin^{-1} y + \sin^{-1} z = \pi$, show that $x^2 - y^2 - z^2 + 2yz\sqrt{1 - x^2} = 0$ 2024 · 4 marks · Derivation
- The value of $\tan^{-1} \sqrt{3} - \sec^{-1}(-2)$ is equal to 2023 · 1 mark · MCQ
- If $\tan^{-1}\left(\frac{x-1}{x+1}\right) + \tan^{-1}\left(\frac{2x-1}{2x+1}\right) = \tan^{-1}\left(\frac{23}{36}\right)$ then… 2023 · 4 marks · Derivation
- Solve for $x$: $5\tan^{-1} x + 3\cot^{-1} x = 2\pi$ 2023 · 2 marks · Short answer
- If $\cos^{-1} \frac{x}{a} + \cos^{-1} \frac{y}{b} = \alpha$, prove that… 2023 · 4 marks · Derivation
- $\forall x \in \mathbb{R}$, $\cot^{-1}(-x) =$ 2022 · 2 marks · MCQ
- If $\alpha \le 2\sin^{-1} x + \cos^{-1} x \le \beta$, then $(\alpha, \beta)$ is: 2022 · 2 marks · MCQ
- What will be the Principal value of $\operatorname{cosec}^{-1}(-\sqrt{2})$? 2022 · 2 marks · MCQ
- Prove that $\tan^{-1}\frac{1}{2} = \frac{\pi}{4} - \frac{1}{2} \cos^{-1}\left(\frac{4}{5}\right)$. 2021 · 4 marks · Derivation
- Simplified value of $\sin\left[\frac{\pi}{2} - \sin^{-1}\left(-\frac{\sqrt{3}}{2}\right)\right]$ is: 2021 · 1 mark · MCQ
- If $\cos^{-1}\frac{x}{2} + \cos^{-1}\frac{y}{3} = \theta$, then prove that $9x^2 - 12xy\cos\theta + 4y^2 = 36\sin^2\theta$. 2020 · 4 marks · Derivation
- Evaluate: $\cos\left(2\cos^{-1} x + \sin^{-1} x\right)$ at $x = \frac{1}{5}$. 2020 · 4 marks · Numerical
- Prove that: $\tan^2(\sec^{-1} 2) + \cot^2(\operatorname{cosec}^{-1} 3) = 11$. 2020 · 2 marks · Derivation
- If $\sec^{-1} x = \operatorname{cosec}^{-1} y$, show that $\frac{1}{x^2} + \frac{1}{y^2} = 1$ 2019 · 4 marks · Derivation
- Solve for $x$: $\tan^{-1}\left(\frac{x - 1}{x - 2}\right) + \tan^{-1}\left(\frac{x + 1}{x + 2}\right) = \frac{\pi}{4}$ 2019 · 4 marks · Short answer
- Solve: $\sin(2\tan^{-1}x) = 1$ 2019 · 2 marks · Short answer
- Prove that $\tan^{-1}\left(\frac{1}{2}\right) = \frac{\pi}{4} - \frac{1}{2} \cos^{-1}\left(\frac{4}{5}\right)$. 2018 · 4 marks · Derivation
- Solve: $3\tan^{-1}x + \cot^{-1}x = \pi$ 2018 · 2 marks · Short answer
- If $\tan^{-1}a + \tan^{-1}b + \tan^{-1}c = \pi$, prove that $a + b + c = abc$. 2018 · 4 marks · Derivation
- Solve: $\sin^{-1}(\cos(\sin^{-1} x)) = \frac{\pi}{3}$ 2018 · 2 marks · Short answer
- Prove that $\frac{1}{2}\cos^{-1}\left(\frac{1-x}{1+x}\right) = \tan^{-1}\sqrt{x}$. 2017 · 3 marks · Derivation
- Solve the equation for $x$: $\sin^{-1} x + \sin^{-1}(1 - x) = \cos^{-1} x, \quad x \neq 0$ 2017 · 5 marks · Short answer
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