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Inverse Trigonometric Functions · Question 110 of 120

Question 110

HardOriginal question

What is the value of tan⁡−1(3)−sec⁡−1(−2)\tan^{-1}\left(\sqrt{3}\right) - \sec^{-1}(-2)?

Options for question 110

Show the answer and explanation
CorrectNot quiteAnswer A

Correct answer: A

Explanation

  1. Take each principal value on its own branch.

  2. π3−2π3=−π3\frac{\pi}{3} - \frac{2\pi}{3} = -\frac{\pi}{3}.

Worth noting

2π3\frac{2\pi}{3} takes sec⁡−1(−2)\sec^{-1}(-2) as −π3-\frac{\pi}{3}; on [0,π][0, \pi] it is 2π3\frac{2\pi}{3}.

Concept
Adding principal values
Typical time
120 s
Your time
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The rule this testsValues of expressions
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Ten questions from Inverse Trigonometric Functions, at your own pace.

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Ten questions from Inverse Trigonometric Functions, at your own pace.

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