AP EAMCET · Maths · Inverse Trigonometric Functions
The range of the real valued function \(f(x)=\operatorname{Cos}^{-1}(-x)+\operatorname{Sin}^{-1}(-x)+\operatorname{Cosec}^{-1}(x)\) is
- A \(\left\{0, \frac{\pi}{2}\right\}\)
- B \(\left[0, \frac{\pi}{2}\right) \cup\left(\frac{\pi}{2}, \pi\right]\)
- C \(\left(0, \frac{\pi}{2}\right)\)
- D \(\{0, \pi\}\)
Answer & Solution
Correct Answer
(D) \(\{0, \pi\}\)
Step-by-step Solution
Detailed explanation
Domain of \(f(x)\): \([-1, 1] \cap ( (-\infty, -1] \cup [1, \infty) ) = \{-1, 1\}\) For \(x=1\): \(f(1) = \operatorname{Cos}^{-1}(-1) + \operatorname{Sin}^{-1}(-1) + \operatorname{Cosec}^{-1}(1) = \pi - \frac{\pi}{2} + \frac{\pi}{2} = \pi\) For \(x=-1\):…
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