1-cos2x Formula, Identity, Proof | Simplify 1-cos2x

The formula of 1-cos2x is given by 1-cos2x=2sin²x. In this post, we establish 1-cos2x formula and identity with some solved examples.

Formula of 1-cos2x

Answer: The 1-cos2x formula is 1-cos2x=2sin²x.

Proof:

Using the formula cos2θ= cos²θ -sin²θ, the given expression can be written as follows.

1-cos2x

= 1- (cos²x -sin²x)

= (1- cos²x) -sin²x

= sin²x -sin²x

= 2sin²x.

Thus, 1-cos2x = 2sin²x.

So the formula of 1-cos2x is given as follows:

$\boxed{1-\cos 2x = 2\sin^2 x}$

Therefore, the simplification of 1-cos2x is 1-cos2x = 2sin²x.

Also Read:

Formula of sec 2x

Formula of cos⁴x + sin⁴x

Question-Answer

Question1: Find the value of 1-cos120°.

Answer:

Using the above formula 1 – cos2x = 2sin²x, we have

1-cos120° = 2sin²60° = 2 × (1/2)² = 2/4 = 1/2.

Thus, the value of 1-cos120° is 1/2.

FAQs