Question

Using the double angle formula, how do you find the function values for `cos^2(pi/12) and sin^2(pi/8)`?

Answer 1

Use the trig identities: `cos 2a = 2.cos^2 a - 1` and
`cos 2a = 1 - 2.sin^2 a`.

`2.cos^2 (Pi/12) = 1 + cos (Pi/6) = 1 + (sqr3)/2 = 1.866.`

`cos^2 (Pi/12) = 1.866/2 = 0.933`

`2.sin^2 (Pi/8) = 1 - cos (Pi/4) = 1 - (sqr2)/2 = 0.293`

`sin^2 (Pi/8) = 0.147.`