MHT CET · Maths · Inverse Trigonometric Functions
If \(\left(\cos ^{-1} x\right)^2-\left(\sin ^{-1} x\right)^2>0\), then
- A \(x < \frac{1}{2}\)
- B \(-1 < x < \sqrt{2}\)
- C \(0 \leqslant x < \frac{1}{\sqrt{2}}\)
- D \(-1 \leqslant x < \frac{1}{\sqrt{2}}\)
Answer & Solution
Correct Answer
(D) \(-1 \leqslant x < \frac{1}{\sqrt{2}}\)
Step-by-step Solution
Detailed explanation
\(\left(\cos ^{-1} x - \sin ^{-1} x\right)\left(\cos ^{-1} x + \sin ^{-1} x\right) > 0\) \(\left(\cos ^{-1} x - \sin ^{-1} x\right)\left(\frac{\pi}{2}\right) > 0\)
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