KCET · Maths · Inverse Trigonometric Functions
If \( a+\frac{\pi}{2} < 2 \tan ^{-1} x+3 \cot ^{-1} x < b \) then ' \( a \) ' and 'b' are respectively.
- A \( \frac{\pi}{2} \) and \( 2 \pi \)
- B \( \frac{\pi}{2} \) and \( \frac{\pi}{2} \)
- C \( 0 \) and
- D \( 0 \) and \( 2 \pi \)
Answer & Solution
Correct Answer
(A) \( \frac{\pi}{2} \) and \( 2 \pi \)
Step-by-step Solution
Detailed explanation
\( 2 \tan ^{-1} x+3 \cot ^{-1} x = 2(\tan ^{-1} x+\cot ^{-1} x) + \cot ^{-1} x \) \( = 2\left(\frac{\pi}{2}\right) + \cot ^{-1} x = \pi + \cot ^{-1} x \)
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