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The value of a for which a x 2 + sin - 1 ⁡ x 2 - 2 x + 2 + cos - 1 ⁡ x 2 - 2 x + 2 = 0 has a real solution, is

Options

  1. A- 2 π
  2. B2 π
  3. C- π 2
  4. Dπ 2

Correct answer

C. - π 2

Step-by-step solution

Here, x 2 - 2 x + 2 = x - 1 2 + 1 ≥ 1 But, - 1 ≤ ( x 2 - 2 x + 2 ) ≤ 1 Which is possible only when x 2 - 2 x + 2 = 1 ⇒ x = 1 Then, a 1 2 + sin - 1 ⁡ 1 + cos - 1 ⁡ 1 = 0 ⇒ a + π 2 + 0 = 0 ⇒ a = - π 2

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