Answer:
Compound angle identities are trigonometric identities that relate the trigonometric functions of the sum or difference of two angles to the trigonometric functions of the individual angles.
The main compound angle identities are:
1. sin(A ± B) = sin(A)cos(B) ± cos(A)sin(B)
2. cos(A ± B) = cos(A)cos(B) ∓ sin(A)sin(B)
3. tan(A ± B) = (tan(A) ± tan(B)) / (1 ∓ tan(A)tan(B))
where A and B are any two angles.
These identities can be used to simplify trigonometric expressions, solve trigonometric equations, and prove other trigonometric identities.
For example, we can use the compound angle identity for sin(A + B) to find sin(π/4 + π/6):
sin(π/4 + π/6) = sin(π/4)cos(π/6) + cos(π/4)sin(π/6)
sin(π/4 + π/6) = (√2/2)(√3/2) + (√2/2)(1/2)
sin(π/4 + π/6) = (√6 + √2) / 4
Compound angle identities are an important part of trigonometry and are used in various fields such as physics, engineering, and mathematics.