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# Integrating (Cos2x)^2 [OCR, C4]

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1. I came across a maths question in an OCR C4 paper that at one point involved integrating Cos22x.

The two identities regarding Cos2x i know of are:
cos2x = 2cos2x - 1 and cos2x= 1-2sin2x

I tried squaring both of those identites but ultimately got nothing that seems like it could be easily integrated eg. 4cos4x-4cos2x+1

The mark scheme says Cos22x = 1/2 (1+cos4x) (which can be easily integrated)

I was just curious to know how they got to 1/2 (1+cos4x), in case a similar question was to come up in the exam.
2. (Original post by MohammedPatel)
I came across a maths question in an OCR C4 paper that at one point involved integrating Cos22x.

The two identities regarding Cos2x i know of are:
cos2x = 2cos2x - 1 and cos2x= 1-2sin2x

I tried squaring both of those identites but ultimately got nothing that seems like it could be easily integrated eg. 4cos4x-4cos2x+1

The mark scheme says Cos22x = 1/2 (1+cos4x) (which can be easily integrated)

I was just curious to know how they got to 1/2 (1+cos4x), in case a similar question was to come up in the exam.
Let A = 2x. This way Cos2A = 2cos^2(A) - 1. Now sub back A = 2x. Can you see it now?
3. (Original post by MohammedPatel)
I came across a maths question in an OCR C4 paper that at one point involved integrating Cos22x.

The two identities regarding Cos2x i know of are:
cos2x = 2cos2x - 1 and cos2x= 1-2sin2x

I tried squaring both of those identites but ultimately got nothing that seems like it could be easily integrated eg. 4cos4x-4cos2x+1

The mark scheme says Cos22x = 1/2 (1+cos4x) (which can be easily integrated)

I was just curious to know how they got to 1/2 (1+cos4x), in case a similar question was to come up in the exam.

Let

Then
4. Thanks guys

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