α = sin 36 ° is a root of which of the following equation

α=sin36° is a root of which of the following equation
  1. 16x4-20x2+5=0
  2. 16x4+20x2+5=0
  3. 10x4-10x2-5=0
  4. 16x4-10x2+5=0

Solution

We know sin36°=10-254

Let x=10-254

On squaring both sides, we get

4x2=10-25⇒16x2=10-25 

Again squaring, we get 

52=5-8x22 ⇒5=25+64x4-80x2

⇒16x4-20x2+5=0

Asked in: JEE Main 2022 (27 Jun Shift 2)

Practice more Trigonometric Ratios & Identities questions on Aicharya