how to split up using sum and difference identities

Question

cos (13pi/12)

PLeaseeeeeeeeeee help!!! thanx a million

Answer 1

Sometimes it is easier for students to see these relationships in degrees.
13π/12 radians = 195°
and 195 = 45+150

Knowing the ratio of sides of the 30-60-90 and the 45-45-90 triangles we can find that
sin 150°=1/2
cos 150° = -√3/2

sin 45° = cos 45° = 1/√2 = √2/2

then back to
cos(13π/12)
= cos(195)
= cos(150+45)
= cos150 cos45 - sin150 sin45
= (-√3/2)(√2/2) - (1/2)(√2/2
= (-√6 - √2)/4