INTEGRATION OF COS SQUARE X

We know the integration of cosine x which is sine x.

When the exponent of cosine is 1, it can be integrated using the stuff given above. If the exponent of cosine is a positive integer greater than 1, we can not find integration directly.

To find the integration of cos square x, we can use the double angle formula of cosine.

cos(2x) = cos²x - sin²x ----(1)

In the above double angle formula, write sin²x in terms of cos²x and solve for cos²x.

We already know that sin²x + cos²x = 1.

Then, we have

sin²x = 1 - cos²x

Substitute sin²x = 1 - cos²x into (1).

cos(2x) = cos²x - (1 - cos²x)

cos(2x) = cos²x - 1 + cos²x

cos(2x) = 2cos²x - 1

1 + cos(2x) = 2cos²x

Integration of Cos Square x

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