Find the Exact Value cos(105 degrees )^2-sin(105 degrees )^2

$\cos^{2} (105 °) - \sin^{2} (105 °)$

Step 1

Apply the cosine double-angle identity.

$\cos (2 \cdot 105 °)$

Step 2

Multiply $2$ by $105 °$ .

$\cos (210)$

Step 3

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the third 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:

$- 0.86602540 \dots$

Find the Exact Value cos(105 degrees )^2-sin(105 degrees )^2

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