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Let $f (θ) = \cos θ \cos 2 θ \cos 4 θ \cos 7 θ$ , then $f (π / 15)$ is equal to

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a

14

b

18

c

116

d

132

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detailed solution

Correct option is C

f(θ)=12sin⁡θ(2sin⁡θcos⁡θ)cos⁡2θcos⁡4θcos⁡7θ=12×2sin⁡θ(2sin⁡2θcos⁡2θ)cos⁡4θcos⁡7θ=12×4sin⁡θ(2sin⁡4θcos⁡4θ)cos⁡7θ=12×8sin⁡θ[2sin⁡8θcos⁡7θ]=116sin⁡θ[sin⁡(15θ)+sin⁡θ]when θ=π15,f(θ)=116

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