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3 votes
Verify the identity:

cos 4x + cos 2x = 2 - 2 sin2 2x - 2 sin2 x

User Yanhan
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2 Answers

1 vote
By using trigonometric identities, we can solve the identity given above. We just need to work on one side and make it equal to the other side. We choose the right side:

2−2sin2(2x)−2sin2(x)=1+1−2sin2(2x)−2sin2(x) = (1−2sin2(2x))+(1−2sin2(x)) + (1−2sin2(2x))+(1−2sin2(x)) =cos(4x)+cos(2x)

cos 4x + cos 2x = cos 4x + cos 2x
User Ahmed Contrib
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8.4k points
3 votes

\\ sin^2 \alpha +cos^2 \alpha =1 \\ cos2 \alpha =1-2sin^2 \alpha \\cos( \alpha + \beta )=cos \alpha cos \beta -sin \alpha sin \beta \\ \\ cos4x=cos(2x+2x)=cos2xcos2x-sin2xsin2x = \\ =cos^22x-sin^22x \\ cos^22x=1-sin^22x \\ cos^22x-sin^22x=1-sin^22x-sin^22x=1-2sin^22x \\ cos4x=1-2sin^22x \\ cos2x =1-2sin^2x \\ \\ cos4x+cos2x=1-2sin^22x+1-2sin^2x= \\ =2-2sin^22x-2sin^2x \\ \\ cos4x+cos2x=2-2sin^22x-2sin^2x
User Nitin Gohel
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8.4k points

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