Find the Exact Value cos(150 degrees )^2-sin(150 degrees )^2

$\cos^{2} (150 °) - \sin^{2} (150 °)$

Step 1

Apply the cosine double-angle identity.

$\cos (2 \cdot 150 °)$

Step 2

Multiply $2$ by $150 °$ .

$\cos (300)$

Step 3

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$\cos (60)$

Step 4

The exact value of $\cos (60)$ is $\frac{1}{2}$ .

$\frac{1}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$