Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 202227 JuneEvening Shift
Exam
JEE Main
Year
2022
Date
27 June
Shift
Evening Shift
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

JEE Main 2022 · 27 June · Evening Shift · Mathematics · Trigonometric Ratios & Identities

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

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

Options

  1. A16x4−20x2+5=016{x}^{4} - 20{x}^{2} + 5 = 0
  2. B16x4+20x2+5=016{x}^{4} + 20{x}^{2} + 5 = 0
  3. C10x4−10x2−5=010{x}^{4} - 10{x}^{2} - 5 = 0
  4. D16x4−10x2+5=016{x}^{4} - 10{x}^{2} + 5 = 0

Correct answer

A. 16x4−20x2+5=016{x}^{4} - 20{x}^{2} + 5 = 0

Step-by-step solution

We know sin⁡36°=10−254\sin 36 ° = \dfrac{\sqrt{10 - 2\sqrt{5}}}{4}

Let x=10−254x = \dfrac{\sqrt{10 - 2\sqrt{5}}}{4}

On squaring both sides, we get

(4x)2=10−25{\left(4x\right)}^{2} = 10 - 2\sqrt{5}⇒16x2=10−25⇒ 16{x}^{2} = 10 - 2\sqrt{5}

Again squaring, we get

(5)2=(5−8x2)2{\left(\sqrt{5}\right)}^{2} = {\left(5 - 8{x}^{2}\right)}^{2} ⇒5=25+64x4−80x2⇒ 5 = 25 + 64{x}^{4} - 80{x}^{2}

⇒16x4−20x2+5=0⇒ 16{x}^{4} - 20{x}^{2} + 5 = 0

Practice Trigonometric Ratios & Identities on Quantrex Academy →

More from Trigonometric Ratios & Identities

Let α = (1 - 2 ((π)/(11)))(1 - 2 ((3π)/(11)))(1 - 2 ((9π)/(11)))(1 - 2 ((27π)/(11)))(1… JEE Advanced 2026If A = ( 3^∘)/( 9^∘) + ( 9^∘)/( 27^∘) + ( 27^∘)/( 81^∘) and B = 81^∘ - 3^∘ , then (B)/(A)… JEE Main 2026Let P = \ θ ∈ [0, 4π] : ^2θ ≠ 1\ and S = \ a ∈ ℤ : 2( ^8θ - ^8θ) 2θ = a^2, θ ∈ P\ . Then… JEE Main 2026If ((π)/(18)) ((5π)/(18)) ((7π)/(18)) = K , then the value of ((10Kπ)/(3)) is : JEE Main 2026If (A-B) A + ^ 2 C ^ 2 ~A =1, ~A, ~B, C ∈(0, (π)/(2)) , then JEE Main 2026If x=(5)/(12) for some x ∈(π, (3 π)/(2)) , then 7 x( (13 x)/(2)+ (13 x)/(2))+ 7 x( (13… JEE Main 2026The value of 3 cosec 20^ ∘ - 20^ ∘ 20^ ∘ 40^ ∘ 60^ ∘ 80^ ∘ is equal to JEE Main 2026The least value of ( ^ 2 θ-6 θ θ+3 ^ 2 θ+2) is JEE Main 2026Let (π)/(2) ((15 θ)/(2))( 8 θ+ 8 θ)+ ((15 θ)/(2))( 8 θ- 8 θ) is equal to JEE Main 2026Let α and β respectively be the maximum and the minimum values of the function f(θ)=4( ^… JEE Main 2026Let (α+β)=-(1)/(10) and (α-β)=(3)/(8) , where 0<α<(π)/(3) and 0<β<(π)/(4) . If 2 α= 3(1-r… JEE Main 2026If ^ 2 48^ ∘ - ^ 2 12^ ∘ ^ 2 24^ ∘ - ^ 2 6^ ∘ = α+β 5 2 , where α, β ∈ ℕ , then α+β is… JEE Main 2026The value of cosec 10^ ∘ - 3 10^ ∘ is equal to : JEE Main 2026Let α= 1 60^ ∘ 61^ ∘ + 1 62^ ∘ 63^ ∘ +…+ 1 118^ ∘ 119^ ∘ Then the value of ( cosec 1^ ∘ α… JEE Advanced 2025If x+ ^2 x=1, x ∈(0, (π)/(2)) , then ( ^ 12 x+ ^ 12 x)+3( ^ 10 x+ ^ 10 x+ ^8 x+ ^8 x)+(… JEE Main 2025If ∑_ r=1 ^ 13 \ (1)/( ((π)/(4)+(r-1) (π)/(6)) ((π)/(4)+(r π)/(6)))\ =a 3 +b, a, b ∈ Z… JEE Main 2025 Full Trigonometric Ratios & Identities list Trigonometric Ratios & Identities JEE Maths PYQsJEE Mathematics PYQs All JEE Main PYQs