Assertion (A): cot^-1(-1) = 3π/4. Reason (R): cot^-1 x = tan^-1 1/x for every x ≠ 0.

Question 58

MediumOriginal question

Assertion (A): $\cot^{-1}(-1) = \frac{3\pi}{4}$ .
Reason (R): $\cot^{-1} x = \tan^{-1} \frac{1}{x}$ for every $x \ne 0$ .

Both A and R are true, and R is the correct explanation of A.Correct answerYour answerBoth A and R are true, but R is not the correct explanation of A.Correct answerYour answerA is true, but R is false.Correct answerYour answerA is false, but R is true.Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

A is true: $\cot \frac{3\pi}{4} = -1$ , and $\frac{3\pi}{4}$ is in $(0, \pi)$ .
R is false: at $x = -1$ it gives $\tan^{-1}(-1) = -\frac{\pi}{4}$ , outside $(0, \pi)$ ; the rule holds only for $x > 0$ .

Worth noting

R swaps $\cot^{-1}$ for $\tan^{-1}$ of the reciprocal, which drops a negative input onto the wrong branch.

Concept: Principal values of related inputs
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsPrincipal values

Practise this chapter →

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

Assertion (A): cot⁡−1(−1)=3π4\cot^{-1}(-1) = \frac{3\pi}{4}cot−1(−1)=43π​.Reason (R): cot⁡−1x=tan⁡−11x\cot^{-1} x = \tan^{-1} \frac{1}{x}cot−1x=tan−1x1​ for every x≠0x \ne 0x=0.

Explanation

Assertion (A): $\cot^{-1}(-1) = \frac{3\pi}{4}$ .
Reason (R): $\cot^{-1} x = \tan^{-1} \frac{1}{x}$ for every $x \ne 0$ .