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Question

The value of 18(3-4cos2θ+cos4θ) is


A

cos4θ

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B

sin4θ

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C

sin4θ

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D

cos4θ

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E

sin4θ2

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Solution

The correct option is C

sin4θ


The explanation for the correct answer.

Given: 18(3-4cos2θ+cos4θ)

Formula cos2A=2cos2A-1

18(3-4cos2θ+cos4θ)=183-4cos2θ+2cos22θ-1=182cos22θ-2·2cos2θ+2=28cos22θ-2cos2θ+1=14cos2θ-12a2-2ab+b2=a-b2=141-2sin2θ-12cos2θ=1-2sin2θ=144sin4θ=sin4θ

Hence option(C) is the correct answer.


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