Solve for exact value using sum or difference indentities?

Question

Solve for cos(pi/12)
All help appreciated.
Thx in advance.

Answer 1

pi/12 = pi/3 - pi/4

cos pi/3 = 1/2
sin pi/3 = sqrt(3)/2

cos pi/4 = sin pi/4 = sqrt(2)/2

cos (pi/12) = cos pi/3 cos pi/4 + sin pi/3 sin pi/4
= (sqrt(2)/2)( 1+ sqrt(3))/2 = (1+sqrt(3)/(2sqrt(2))

Answer 2

We know that pi/6 or 30degrees is the angle in a right angled triangle with sides of 1, 2, sqrt3. Therefore sin(pi/6) = 1/2 and cos(pi/6) = (sqrt3)/2. You therefore need to use the double angle formulas for cos or sin to break one of these up into pi/12. (Hint cos is easier.)

Answer 3

cos (pi/6 -pi/4)= cos(pi/6)cos(pi/4)+sin(pi/6)sin(pi/4)
=(√3/2)(1/√2)+(1/2)(1/√2)
=(√3+1)/2√2
rationalize
= (√6+√2)/4