Let f ( )=3( sin^4( 2- )+ sin^4(3 + ))-2(1- sin^22 ) and S=( ϵ (0 , ) :f^ ' ( )=- 32). If 4 = then f ( ) is equal to

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Correct answer: B. (b) Solution f ( )=3( sin^4( 3 2- )+ sin^4(3x+ ))-2 (2- sin^22 ) S=( ϵ (0 , ) :t^-1 ( )=- 32) ⇒f ( )-3( cos^2 + sin^4 )-2 cos^22 θπ ⇒f ( )=33(1- 12 sin^22 )+2 cos^22 ⇒f ( )=3- 32 sin^22 -2 cos^2 = 32- 12 cos^22 = 32+ 12 ( 1+ cos4 2 ) ⇒ f ( )= 54- cos4 4 f ( )= sin4 ⇒f^ ' ( )- sin4 - 32 ⇒4 = nπ+(-1)^n 3 ⇒ - nπ4+(-1)^1 32 θπ ⇒ - 12 .( 4- 12) .( 2+ 12) .( 3 4- 12) ⇒4 = 4+ 2+ 3 4= 3 2 ⇒ = 3 8 ⇒f ( )= 54- cos 3 24= 54

$Let f (θ) = 3 (sin^{4} (\frac{π}{2} - θ) + sin^{4} (3 π + θ)) - 2 (1 - sin^{2} 2 θ) and S = (θ ϵ (0, π) : f^{’} (θ) = - \frac{3}{2}) . If 4 β = \sum θ then f (β) is equal to$

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