If E = ^ 2 71 ^ o + ^ 2 49 ^ o + cos 71 ^ o cos 49 ^ o , then the value of 10E is equal to

Correct answer: A. 7. 5 E = 1 + cos 142 ^ o 2 + 1 + cos 98 ^ o 2 + (1)/(2) (2cos 71 ^ o cos 49 ^ o ) = 1 + (1)/(2)(cos 142 ^ o + cos 98 ^ o ) + (1)/(2)(cos 120 ^ o + cos 22 ^ o ) = 1 + (1)/(2) (2cos 120 ^ o cos 22 ^ o ) + (1)/(2)(- (1)/(2) + cos 22 ^ o ) = 1 + (- (1)/(2)) cos 22 ^ o - (1)/(4) + (1)/(2) cos 22 ^ o = (3)/(4) E = (3)/(4) =0.75 ⇒ 10E = 7.5

NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Mathematics
Chapter: Trigonometric Ratios & Identities

NTA Abhyas 2020 · Mathematics · Trigonometric Ratios & Identities

If E = ^ 2 71 ^ o + ^ 2 49 ^ o + cos 71 ^ o cos 49 ^ o , then the...

E = \cos^{2} {71}^{o} + \cos^{2} {49}^{o} + cos {71}^{o}cos {49}^{o},

then the value of

10E

is equal to

Options

A $7. 5$
B $2. 5$
C $12. 5$
D $10. 5$

Correct answer

A. $7. 5$

Step-by-step solution

E = \dfrac{1 + cos {142}^{o}}{2} + \dfrac{1 + cos {98}^{o}}{2} + \dfrac{1}{2} \left(2cos {71}^{o}cos {49}^{o}\right)

= 1 + \dfrac{1}{2}\left(cos {142}^{o} + cos {98}^{o}\right) + \dfrac{1}{2}\left(cos {120}^{o} + cos {22}^{o}\right)

= 1 + \dfrac{1}{2} \left(2cos {120}^{o}cos {22}^{o}\right) + \dfrac{1}{2}\left(- \dfrac{1}{2} +

cos {22}^{o}\right)

<br />

= 1 + \left(- \dfrac{1}{2}\right)

cos {22}^{o} -

\dfrac{1}{4} + \dfrac{1}{2} cos {22}^{o} = \dfrac{3}{4}$

<br />

E =

\dfrac{3}{4} =0.75

$⇒ 10E = 7.5

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