Find the Exact Value 1-2sin(165 degrees )^2

$1 - 2 \sin^{2} (165 °)$

Step 1

Apply the cosine double-angle identity.

$\cos (2 \cdot 165 °)$

Step 2

Multiply $2$ by $165 °$ .

$\cos (330)$

Step 3

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

$\cos (30)$

Step 4

The exact value of $\cos (30)$ is $\frac{\sqrt{3}}{2}$ .

$\frac{\sqrt{3}}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{3}}{2}$

Decimal Form:

$0.86602540 \dots$