Question

Trig. help. How does 29%20%3D%20sinx" id="TexFormula1" title="2sin (\frac{1}{2} x)cos( \frac{1}{2} x) = sinx" alt="2sin (\frac{1}{2} x)cos( \frac{1}{2} x) = sinx" align="absmiddle" class="latex-formula"> ?

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.