Sections:

Trigonometric Identities and Equations, Page 16

Sum and Difference Identities

The next set of identities is the Sum and Difference Identities for sine, cosine, and tangent.

sin(α ± β) = sinα cosβ ± cosα sinβ; cos(α ± β) = cosα cosβ - or + sinα sinβ; tan(α ± β) = (tanα ± tanβ)/(1 - or + tanα tanβ)

If you are given x = pi/3 and y = pi/6; find cos(x - y).

Use the Difference Identity of Cosine: 

cos(α - β) = cosα cosβ + sinα sinβ; cos(pi/3 - pi/6) = cos(pi/3) cos(pi/6) + sin(pi/3) sin(pi/6); cos(pi/3 - pi/6) = (1/2)(sqrt(3)/2) + (sqrt(3)/2)(1/2); cos(pi/3 - pi/6) = sqrt(3)/4 + sqrt(3)/4 = 2sqrt(3)/4 = sqrt(3)/2