Answer:
[tex]-\frac{\sqrt{2}}{2}[/tex]
Step-by-step explanation:
[tex]\cos^2(x)-\sin^2(x)=\cos(2x)[/tex] by the double angle identity for cosine.
Therefore, [tex]\cos^2(67.5)-\sin^2(67.5)=\cos(2 \cdot 67.5)=\cos(135)[/tex].
Now to finish the problem we just need to look at our handy dandy unit circle in the second quadrant.
It should say the [tex]x[/tex]-coordinate at [tex]135^\circ[/tex] is [tex]-\frac{\sqrt{2}}{2}[/tex].
