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AP EAMCET202119 Aug 2021Evening ShiftMathematicsInverse Trigonometric FunctionsActual

For how many distinct values of x , the equation sin 2 cos - 1 cot 2 tan - 1 x = 0 holds?

Options

  1. A8
  2. B2
  3. C6
  4. D4

Correct answer

C. 6

Step-by-step solution

Given, sin 2 cos - 1 cot 2 tan - 1 x = 0 Let tan - 1 x = y ⇒ x = tan y Then, sin 2 cos - 1 cot 2 y = 0 ⇒ sin 2 cos - 1 1 - tan 2 y 2 tan y = 0 ⇒ sin 2 cos - 1 1 - x 2 2 x = 0 ⇒ sin cos - 1 2 1 - x 2 2 x 2 - 1 = 0 ⇒ sin sin - 1 1 - 2 1 - x 2 2 x 2 - 1 2 = 0 ⇒ 1 - 2 1 - x 2 2 x 2 - 1 2 = 0 ⇒ 1 - 2 1 - x 2 2 x 2 - 1 2 = 0 ⇒ 2 1 - x 2 2 x 2 - 1 2 = 1 ⇒ 2 1 - x 2 2 x 2 - 1 = ± 1 ⇒ 2 1 - x 2 2 x 2 = 1 ± 1 = 2 ,   0 ⇒ 2 1 - x 2 2 x 2 = 2 or 2

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