Question

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

Answer 1

`-(√(2))/(2)`

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
`-(√(2))/(2)`.