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Inverse Trigonometric Functions Maths - Inverse Trigonometric Functions

Gujarat Board (GSEB) - STD 12 Science - Maths (GSEB - English Medium). 37 questions in this chapter.

Question types

Inverse Trigonometric Functions question types

37 questions across 5 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

37
Questions
5
Question groups
5
Question types
Sample Questions

Inverse Trigonometric Functions questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 2M.C.Q (1 Marks)1 Mark
The principal value of $\tan ^{-1}\left(\tan \frac{9 \pi}{8}\right)$ :
  • ✓
    $\frac{\pi}{8}$
  • B
    $\frac{3 \pi}{8}$
  • C
    $\frac{-\pi}{8}$
  • D
    $\frac{-3 \pi}{8}$

Answer: A.

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Q 3M.C.Q (1 Marks)1 Mark
The principal value of $\cos ^{-1}\left(\frac{1}{2}\right)+\sin ^{-1}\left(\frac{-1}{\sqrt{2}}\right)$
  • ✓
    $\frac{\pi}{12}$
  • B
    $\pi$
  • C
    $\frac{\pi}{3}$
  • D
    $\frac{\pi}{6}$

Answer: A.

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Q 4M.C.Q (1 Marks)1 Mark
The value of $\sin ^{-1}\left(\frac{\sqrt{3}}{2}\right)+2 \cos ^{-1}\left(\frac{\sqrt{3}}{2}\right)$ :
  • A
    $\frac{\pi}{2}$
  • B
    $\frac{\pi}{3}$
  • ✓
    $\frac{2 \pi}{3}$
  • D
    $\pi$

Answer: C.

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Q 173 Marks3 Marks
If $\cos ^{-1} \alpha+\cos ^{-1} \beta+\cos ^{-1} \gamma=3 \pi$ then find the value of $\alpha(\beta+\gamma)+\beta(\gamma+\alpha)+\gamma(\alpha+\beta)$
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Q 184 Marks4 Marks
Prove that :\[\tan ^{-1}\left\{\frac{\sqrt{1+\cos x}+\sqrt{1-\cos x}}{\sqrt{1+\cos x}-\sqrt{1-\cos x}}\right\}=\frac{\pi}{4}+\frac{x}{2}, 0 < x <\frac{\pi}{2}\]
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Q 194 Marks4 Marks
Prove that $2 \tan ^{-1}\left\{\sqrt{\frac{\alpha-\beta}{\alpha+\beta}} \tan \frac{x}{2}\right\}=\cos ^{-1}\left(\frac{\beta+\alpha \cos x}{\alpha+\beta \cos x}\right)$
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Q 204 Marks4 Marks
Write in the simplest form $\cos ^{-1}\left(\frac{3}{5} \cos x+\frac{4}{5} \sin x\right)$, where $\frac{\pi}{2} \leq x \leq \frac{3 \pi}{4}$.
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Q 214 Marks4 Marks
If $x, y, z \in[-1,1]$ such that $\sin ^{-1} x+\sin ^{-1} y+$ $\sin ^{-1} z=\frac{-3 \pi}{2}$ then find the value of $x^2+y^2+z^2$.
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Q 224 Marks4 Marks
If $\cos ^{-1} \frac{x}{a}+\cos ^{-1} \frac{y}{b}=\alpha$ then prove that$\frac{x^2}{a^2}-\frac{2 x y}{a b} \cos \alpha+\frac{y^2}{b^2}=\sin ^2 \alpha$
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