Question

Use the fact that cos (pi/6) = sqrt (3)/2 and the formula for the square root to find a formula for cos (pi/12) and sin (pi/12). What will then be the formula for cos (pi/3 * 2 ^ n)) for n = 1,2,3 ...?

Answer 1

This is Trigonometry right?

Answer 2

it appears you want to use the angle difference relation: cos(π/12) = cos(π/4 - π/6). That works also, but you need to get the formula right, which is:

cos(a - b) = cos a * cos b + sin a * sin b

For cos (45 - 30), this gives cos 45 * cos 30 + sin 45 * sin 30 = √2/2 * √3/2 + √2/2 * 1/2 = √2/4(√3 + 1). This is yet another expression for the same exact value.