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JEE Main202131 Aug 2021Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

cosec 18 ° is a root of the equation:

Options

  1. Ax 2 - 2 x - 4 = 0
  2. B4 x 2 + 2 x - 1 = 0
  3. Cx 2 + 2 x - 4 = 0
  4. Dx 2 - 2 x + 4 = 0

Correct answer

A. x 2 - 2 x - 4 = 0

Step-by-step solution

We know that sin 18 ° = 5 - 1 4 cosec 18 ° = 1 sin 18 °   =   4 5 - 1 Rationalizing denominator = 4 5 - 1 × 5 + 1 5 + 1 = 4 5 + 1 4 = 5 + 1 Hence equation x = 5 + 1 ⇒ ( x - 1 ) 2 = 5 ⇒ x 2 - 2 x + 1   =   5 ⇒ x 2 - 2 x - 4 = 0

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