eoluwemimo eoluwemimo
  • 26-02-2020
  • Mathematics
contestada

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

Respuesta :

freckledspots freckledspots
  • 26-02-2020

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].

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