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NTA Abhyas JEE Main2020MathematicsInverse Trigonometric FunctionsPractice

If x = s i n 2 t a n - 1 3 and y = sin 1 2 tan - 1 4 3 , then

Options

  1. A2 x = 1 - y
  2. Bx 2 = 1 - 2 y
  3. Cx 2 = 1 + y
  4. Dy 2 = 2 x - 1

Correct answer

D. y 2 = 2 x - 1

Step-by-step solution

Let, x = sin ⁡ 2 θ (where tan ⁡ θ = 3 ) ⇒ x = 2 tan ⁡ θ 1 + t a n 2 θ = 6 1 + 9 = 3 5 If α = t a n - 1 4 3   ⇒ y = sin α 2 = 1 2 1 - cos α = 1 2 1 - 3 5 = 1 5 ∴ y 2 = 1 5 ⇒ y 2 = 2 x - 1

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