Question

How do you find the exact value of `[cos((5pi)/6)]^2-[sin((5pi)/6)]^2`?

Answer 1

`1/2`

Explanation:

From trig identity:
`cos^2 a - sin^2 a = cos 2a`, we get in this case:
`cos^2 ((5pi)/6) - cos^2 ((5pi)/6) = cos ((10pi)/6) = cos ((5pi)/3)`
On the trig unit circle -->
`cos ((5pi)/3) = cos (pi/3) = 1/2`