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If s i n 2 x + 10 - x 2 = 9 - x 2 + 2 s i n 2 x + c o s 2 x , then x lies in

Options

  1. A- 8,8
  2. B- 3,3
  3. C- 17 , 17
  4. D- 21 , 21

Correct answer

B. - 3,3

Step-by-step solution

s i n 2 x + 10 - x 2 = 9 - x 2 + s i n 2 x + s i n 2 x + c o s 2 x ⇒ s i n 2 x + 1 + 9 - x 2 = 9 - x 2 + s i n 2 x + 1 x + y + z = x + y + z , if x ,   y ,   z have the same sign ⇒ s i n 2 x 9 - x 2 ≥ 0 ⇒ 9 - x 2 ≥ 0 ⇒ x ∈ - 3,3

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