Question

Use the squared identities to simplify sin^2x cos^2x

Answer 1

`(1-cos^2(2x))/(4)`

Explanation:

We have the following expression

`sin^2x *cos^2x`

Whe know that:

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

Now replace these equations in the main expression and simplify

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

`(((1-cos(2x))(1+cos(2x)))/(4))`

Apply the following property

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

Then

`(((1-cos(2x))(1+cos(2x)))/(4))=(1^2-cos^2(2x))/(4)`

Finally:

`(((1-cos(2x))(1+cos(2x)))/(4))=(1-cos^2(2x))/(4)`