Trig. help. How does 2sin ((1)/(2) x)cos( (1)/(2) x) = sinx ?

Question

Trig. help. How does
`2sin ((1)/(2) x)cos( (1)/(2) x) = sinx` ?

Answer 1

Recall that 2sin(x) cos(x) is actually equal to sin(2x).

We can prove this by expanding sin(2x) to sin(x + x).
sin(x + x) = sin(x) cos(x) + cos(x) sin(x) = 2sinxcosx

Thus, 2sin(x/2)cos(x/2) can be rewritten in the form:
sin(2x/2), and this simplifies down to sinx.