Common Half angle identity:
1. sin a = 2 sin (a/2)* cos (a/2)
Half angle Identities in term of t = tan a/2.
2. sin a = (2t)/(1 + t^2)
3.cos a = (1 - t^2)/(1 + t^2)
- tan a = (2t)/(1 - t^2).
Use of half angle identities to solve trig equations.
Example. Solve cos x + 2*sin x = 1 + tan (x/2).
Solution. Call t = tan (x/2). Use half angle identities (2) and (3) to transform the equation.
(1 - t^2)/4 + (1 + t^2)/4 = 1 + t.
1 - t^2 + 4t = (1 + t)(1 + t^2)
t^3 + 2t^2 - 3t = t*(t^2 + 2t - 3) = 0.
Next, solve the 3 basic trig equations: tan (x/2) = t = 0; tan (x/2) = -3; and tan (x/2) = 1.
