Question

Use the squared identities to simplify 2sin2x cos2x. Check below.

Answer 1

`2\sin^2 x\cos^2 x=(1-(\cos 2x)^2)/(2)`

Explanation:

Given : Expression -
`2\sin^2 x\cos^2 x`

To simplify : The given expression?

Solution :

Expression -
`2\sin^2 x\cos^2 x`

Apply the squared identity of the trigonometric function,

`\sin^2 \theta=(1-\cos 2\theta)/(2)`

`\cos^2 \theta=(1+\cos 2\theta)/(2)`

Substitute the value in the given expression,

`=2\sin^2 x\cos^2 x`

`=2* (1-\cos 2x)/(2)* (1+\cos 2x)/(2)`

`=((1-\cos 2x)(1+\cos 2x))/(2)`

Apply,
`a^2-b^2=(a+b)(a-b)`

`=(1^2-(\cos 2x)^2)/(2)`

`=(1-(\cos 2x)^2)/(2)`

Therefore,
`2\sin^2 x\cos^2 x=(1-(\cos 2x)^2)/(2)`

Answer 2

To simplify 2sin2x cos2, you need to use (1 - cos(4x))/4. The correct answer between all the choices given is the first choice or letter A. I am hoping that this answer has satisfied your query about and it will be able to help you.