Verified Solution • 2025–26 Session moderate

QJEEM21Ma6e0a: JEE Main 2021 Mathematics - Class 11 JEEM21Ma6e0a Solution: cosec18 is a root of the equation :

cosec18 ∘^\circ is a root of the equation :

Multiple Choice Options

  • A x2 + 2x −- 4 = 0
  • B 4x2 + 2x −- 1 = 0
  • C x2 −- 2x + 4 = 0
  • D x2 −- 2x −- 4 = 0

Step-by-Step Verified Solution

cos⁡ec18∘=1sin⁡18∘=45−1=5+1\cos ec18^\circ = {1 \over {\sin 18^\circ }} = {4 \over {\sqrt 5 - 1}} = \sqrt 5 + 1

Let cos⁡ec18∘=x=5+1\cos ec18^\circ = x = \sqrt 5 + 1

⇒x−1=5\Rightarrow x - 1 = \sqrt 5

Squaring both sides, we get

x2−2x+1=5{x^2} - 2x + 1 = 5

⇒x2−2x−4=0\Rightarrow {x^2} - 2x - 4 = 0

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