Trigonometry Quiz
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Questions and Answers

How many solutions does the equation $(\cot^{-1}x)^2 - 3(\cot^{-1}x) + 2 > 0$ have?

  • $(\cot 1, \infty)$ (correct)
  • $(\cot 2, \cot 1)$
  • $(-\infty, \cot 1) \cup (\cot 2, \infty)$
  • $(-\infty, \cot 2) \cup (\cot 1, \infty)$
  • What is the value of $\cos\left(\cos^{-1}\left(-\frac{1}{2}\right) + \sin\left(\sin^{-1}\left(-\frac{1}{2}\right)\right)\right)$?

  • $\frac{5\pi}{3}$
  • 2
  • 3
  • 0 (correct)
  • If $1 < x < 2$, then the number of solutions of the equation $\tan^{-1}(x - 1) + \tan^{-1}x + \tan^{-1}(x + 1) = \tan^{-1}3x$ is/are:

  • 2
  • 3
  • 1 (correct)
  • 0
  • What is the complete solution set of $\tan(\sin x) > 1$?

    <p>$\left(-\frac{\pi}{6}, -2\right) \cup \left(\frac{\pi}{6}, 2\right)$</p> Signup and view all the answers

    If $\sin^{-1}\left(\frac{x-1}{2}\right) + \cos^{-1}\left(\frac{x+1}{2}\right) = \frac{\pi}{4}$, then what is $x(x+1) + \sin^{-1}x$?

    <p>$\frac{7}{16}$</p> Signup and view all the answers

    Study Notes

    Trigonometric Equations and Inequalities

    Equation Solving

    • The equation $(\cot^{-1}x)^2 - 3(\cot^{-1}x) + 2 > 0$ has a certain number of solutions.
    • The value of $\cos\left(\cos^{-1}\left(-\frac{1}{2}\right) + \sin\left(\sin^{-1}\left(-\frac{1}{2}\right)\right)\right)$ is a specific number.

    Inverse Trigonometric Functions

    • The number of solutions of the equation $\tan^{-1}(x - 1) + \tan^{-1}x + \tan^{-1}(x + 1) = \tan^{-1}3x$ is dependent on the condition $1 < x < 2$.

    Trigonometric Inequalities

    • The complete solution set of the inequality $\tan(\sin x) > 1$ is a specific set of values.

    Compositions of Inverse Trigonometric Functions

    • The equation $\sin^{-1}\left(\frac{x-1}{2}\right) + \cos^{-1}\left(\frac{x+1}{2}\right) = \frac{\pi}{4}$ is related to the expression $x(x+1) + \sin^{-1}x$.

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    Test your knowledge with this quiz from a trusted institute of DPP JEE-Main, Advance, and NEET. Challenge yourself with questions on trigonometric functions, inverse trigonometric functions, and solving trigonometric equations.

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