Double Angle Identities
sin(2A) = 2sin(A)cos(A)
cos(2A) = cos2(A) - sin2(A)
Addition Subtraction Identities
sin(A B) = sin(A)cos(B) cos(A)sin(B)
cos(A B) = cos(A)cos(B) sin(A)sin(B)
tan(2A) =
tan(A
B) =
Half-Angle Identities
1. Verify the identity:
.
hint: begin with right side and convert to sines and cosines.
sin
cos
tan
2. Verify the identity:
3. If sin(A) =
.
2
5
and A is in quadrant III and cos(B) = 
with B in quadrant III , use the
3
13
identities to find the exact values:
a) cos(A + B)
b) tan(A + B)
c) sin(2A)
d) cos
4. Without using a calculator, use the half-angle identity to find the exact value sin(22.5⁰ .
5. Without using a calculator, use the half-a gle de t ty t f d the exa t value
6. Verify the identity: sin(4x) = (cosx)(4sinx - 8sin3x).
165⁰ .