Maths · Inverse trigonometrical functions and their properties
Solve: \) is real if
Solve: \( \operatorname{cosec}^{-1}(\cos x) \) is real \( , \) if
- A. \( x \in[-1,1] \)
- B. \( x \in R \)
- C. \( x \) is an odd multiple of \( \frac{\pi}{2} \)
- D. x is a multiple of \( \pi \)
Step-by-step solution
cosec^{-1}(y) is real only if |y| ≥ 1. Here y = cos x, and |cos x| ≤ 1. Equality holds only when |cos x| = 1, i.e., cos x = ±1. This occurs when x = nπ, n ∈ Z. Thus x must be a multiple of π.
Related MCQs
- Assertion Consider =\sin ^{-1}\left(\sec \left(\tan ^{-1} \boldsymbol{x}\right)+\right. \) \right. \) Statement-1: Domain of \) is a singlet…
- If value of which satisfy equation ^{2}-3\left(\cot ^{-1} x\right)+2>0 \) is or Find the value of…
- The number of real solutions of the equation }+ \) is…
- Assertion \) If then +\cos ^{-1}(\sin x)=\pi-2 x \) Reason \cos ^{-1} x=\frac{\pi}{2}-\sin ^{-1} x \forall x \in \) \)…
- Assertion then Reason \)…