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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

  1. A 4
  2. B 6
  3. C 8
  4. D Infinitely many
Verified Solution

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, \( 0 \le 2 \operatorname{Cos}^{-1}(u) \le 2\pi \). \( n\pi \in [0, 2\pi] \Rightarrow n \in \{0, 1, 2\} \).…