Question

How do you use a half-angle formula to simplify `cos [ - (3pi) / 8]`?

Answer 1

Use the trig identity: `1 + cos 2x = 2cos^2x`

`2cos^2((-3pi)/8) = 1 - cos ((-3pi)/4)`

Or `cos ((-3pi)/4) = cos ((3pi)/4) = -cos (pi/4)`, then

`2cos^2 (-(3pi)/8) = 1 + cos (pi/4)= 1 + (sqrt2)/2`

`cos^2((-3pi)/8) = (2 + sqrt2)/4`