Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NTA Abhyas 2020 · Mathematics · Trigonometric Ratios & Identities

The expression 27 ° 57 ° 87 ° simplifies to

The expression sin⁡27°cos⁡57°sin⁡87°\sin 27 °\cos 57 °\sin 87 ° simplifies to

Options

  1. Asin⁡9°4\dfrac{\sin 9 °}{4}
  2. Bcos⁡9°4\dfrac{\cos 9 °}{4}
  3. Csin⁡9°2\dfrac{\sin 9 °}{2}
  4. Dcos⁡9°2\dfrac{\cos 9 °}{2}

Correct answer

B. cos⁡9°4\dfrac{\cos 9 °}{4}

Step-by-step solution

sin⁡27°cos⁡57°sin⁡(90°−3°)<br/>=12sin⁡27°(2cos⁡57°cos⁡3°)<br/>=12\sin 27 °\cos 57 °\sin \left(90 ° - 3 °\right)<br />=\dfrac{1}{2} \sin 27 ° \left(2\cos 57 °\cos 3 °\right)<br />=\dfrac{1}{2}\sin 27 ° \left(\cos 60 ° + \cos 54 °\right)<br/><br />= \dfrac{1}{2}sin⁡27°(12)+12\sin 27 ° \left(\dfrac{1}{2}\right) + \dfrac{1}{2}\sin 27 ° \sin 36 °<br/>=14sin⁡27°+14(2sin⁡27°sin⁡36°)<br/>=14<br />=\dfrac{1}{4} \sin 27 ° + \dfrac{1}{4}\left(2\sin 27 ° \sin 36 °\right)<br />=\dfrac{1}{4}\sin 27 ° + 14(cos⁡9°−cos⁡63°)<br/>=14sin⁡27°+14\dfrac{1}{4} \left(\cos 9 ° - \cos 63 °\right)<br />=\dfrac{1}{4} \sin 27 ° + \dfrac{1}{4}\cos 9 ° - 14\dfrac{1}{4} \sin 27 °<br/>=14<br />=\dfrac{1}{4} \cos 9 °
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 NTA Abhyas JEE Main PYQs