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AP EAMCET201825 Apr 2018Morning ShiftMathematicsInverse Trigonometric FunctionsActual

If cos - 1 x 2 + cos - 1 y 3 = θ , then 9 x 2 - 12 x y cos θ + 4 y 2 =

Options

  1. A36 sin 2 θ
  2. B37 sin 2 θ
  3. C39 sin 2 θ
  4. D36 cos 2 θ

Correct answer

A. 36 sin 2 θ

Step-by-step solution

Given: cos - 1 x 2 + cos - 1 y 3 = θ ⇒ cos - 1 x 2 y 3 - 1 - x 2 4 1 - y 2 9 = θ ⇒ x 2 y 3 - 4 - x 2 4 9 - y 2 9 = cos θ ⇒ x y 6 - 4 - x 2 2 9 - y 2 3 = cos θ ⇒ x y - 4 - x 2 · 9 - y 2 = 6 cos θ ⇒ 4 - x 2 · 9 - y 2 = x y - 6 cos θ Squaring both sides, we get 4 - x 2 · 9 - y 2 = 36 cos 2 θ + x 2 y 2 - 12 x y cos θ ⇒ 36 - 9 x 2 - 4 y 2 + x 2 y 2 = 36 cos 2 θ + x 2 y 2 - 12 x y cos θ ⇒ 36 - 36 cos 2 θ = 9 x

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