Half-Angle Formulas

Question

Simplify for x in the third quadrant:

(sin x/2-cos x/2)^2

Answer 1

[sin(x/2) - cos(x/2)]² = sin²(x/2) - 2sin(x/2)(cos(x/2) + cos²(x/2)

= 1 - sin[2(x/2)] = 1 - sinx