Question

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

Answer 1

Answer:

$\frac{1-cos^2(2x)}{4}$

Step-by-step explanation:

We have the following expression

$sin^2x *cos^2x$

Whe know that:

$sin^2(x) = \frac{1-cos(2x)}{2}\\\\cos^2(x)=\frac{1+cos(2x)}{2}$

Now replace these equations in the main expression and simplify

$(\frac{1-cos(2x)}{2})*(\frac{1+cos(2x)}{2})$

$(\frac{(1-cos(2x))(1+cos(2x))}{4})$

Apply the following property

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

Then

$(\frac{(1-cos(2x))(1+cos(2x))}{4})=\frac{1^2-cos^2(2x)}{4}$

Finally:

$(\frac{(1-cos(2x))(1+cos(2x))}{4})=\frac{1-cos^2(2x)}{4}$