Simplify cos(x)^2-cos(x)^2sin(x)^2

$\cos^{2} (x) - \cos^{2} (x) \sin^{2} (x)$

Step 1

Multiply by $1$ .

$\cos^{2} (x) \cdot 1 - \cos^{2} (x) \sin^{2} (x)$

Step 2

Simplify with factoring out.

Factor $\cos^{2} (x)$ out of $- \cos^{2} (x) \sin^{2} (x)$ .

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

Factor $\cos^{2} (x)$ out of $\cos^{2} (x) \cdot 1 + \cos^{2} (x) (- 1 \sin^{2} (x))$ .

$\cos^{2} (x) \cdot (1 - 1 \sin^{2} (x))$

Rewrite $- 1 \sin^{2} (x)$ as $- \sin^{2} (x)$ .

$\cos^{2} (x) \cdot (1 - \sin^{2} (x))$

Step 3

Apply pythagorean identity.

$\cos^{2} (x) \cdot \cos^{2} (x)$

Step 4

Multiply $\cos^{2} (x)$ by $\cos^{2} (x)$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${\cos (x)}^{2 + 2}$

Add $2$ and $2$ .

$\cos^{4} (x)$