### Answer:

1 + cos.2x = 2cos2x

1 – cos2x = 2sin²x

The cos2x formula is essentially used to resolve the integration problems. It will be used as

cos2x = (cos2x + 1)/2.

If you want to solve the integral of (1 – cos2x) and (1 + cos2x). Both mathematical terms will be calculated with the help of trigonometric identities.

- We have cos2x= 1- 2 sin² x. It is a very famous identity to find out any angle x
- Apart from this, another famous identity for cos2x = 2 cos2 x-1. It contains the derivations of identities
- The identity of the cos(2x)= 1- 2 sin² (x)
- You can prove it with 1- cos(2x) = (1- (1-2sin² (x)). Like this, it implies that 1-cos(2x) =2 sin² (x)
- After this, it implies 1-cos(2x)= 2sin² (x)
- In the end, by using all the above-given steps you can easily identify it

Lastly, the formula for 1 + cos2x is 1 + cos2x = 2cos2x. You can prove it very easily with the help of various derivatives and integrals. The formula of 1 – cos2x is 1 – cos2x = 2sin²x. Through this, you can identify trigonometric identities. All these are the terms that help you to find an accurate answer to your question.