Trigonometry Examples

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

Step 1

Simplify terms.

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

Use the double-angle identity to transform $\cos (2 x)$ to $2 \cos^{2} (x) - 1$ .

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

Step 1.1.2

Apply the distributive property.

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

Step 1.1.3

Multiply $2$ by $- 1$ .

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

Step 1.1.4

Multiply $- 1$ by $- 1$ .

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

Step 1.2

Simplify by adding terms.

Tap for more steps...

Step 1.2.1

Subtract $2 \cos^{2} (x)$ from $\cos^{2} (x)$ .

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

Step 1.2.2

Reorder $- \cos^{2} (x)$ and $1$ .

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

Step 2

Apply pythagorean identity.

$\sin^{2} (x)$