MHT CET · Maths · Inverse Trigonometric Functions
If \(\left(\tan ^{-1} x\right)^2+\left(\cot ^{-1} x\right)^2=\frac{5 \pi^2}{8}\), then \(x^2+1=\)
- A \(-1\)
- B 2
- C 1
- D \(-2\)
Answer & Solution
Correct Answer
(B) 2
Step-by-step Solution
Detailed explanation
Let \( \tan^{-1} x = y \). Then \( \cot^{-1} x = \frac{\pi}{2} - y \). \( y^2 + \left(\frac{\pi}{2} - y\right)^2 = \frac{5\pi^2}{8} \)
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