AP EAMCET · Maths · Trigonometric Equations
The number of solutions of the equation \(\sin \left[2 \operatorname{Cos}^{-1}\left\{\cot \left(2 \operatorname{Tan}^{-1} x\right)\right\}\right]=0\) is
- A 4
- B 6
- C 8
- D Infinitely many
Answer & Solution
Correct Answer
(B) 6
Step-by-step Solution
Detailed explanation
\( 2 \operatorname{Cos}^{-1}\left\{\cot \left(2 \operatorname{Tan}^{-1} x\right)\right\} = n\pi \) Range of \( \operatorname{Cos}^{-1}(u) \) is \( [0, \pi] \). Thus, \( 0 \le 2 \operatorname{Cos}^{-1}(u) \le 2\pi \). \( n\pi \in [0, 2\pi] \Rightarrow n \in \{0, 1, 2\} \).…
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