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Mkey [24]
4 years ago
7

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

Mathematics
1 answer:
eimsori [14]4 years ago
4 0

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}.

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