Question

Evaluate cos^2(67.5 degrees) - sin^2(67.5 degrees)

Answer 1

Answer:

$-\frac{\sqrt{2}}{2}$

Step-by-step explanation:

$\cos^2(x)-\sin^2(x)=\cos(2x)$ by the double angle identity for cosine.

Therefore, $\cos^2(67.5)-\sin^2(67.5)=\cos(2 \cdot 67.5)=\cos(135)$.

Now to finish the problem we just need to look at our handy dandy unit circle in the second quadrant.

It should say the $x$-coordinate at $135^\circ$ is $-\frac{\sqrt{2}}{2}$.