Question

How do you prove `sinθ/cos(0.5θ) = 2sin(0.5θ)`?

Answer 1

Since `sin2alpha=2sinalphacosalpha`, double-angle formulae,

`sintheta=2sin(theta/2)cos(theta/2)`

So:

`sintheta/cos(theta/2)=(2sin(theta/2)cos(theta/2))/cos(theta/2)=`

`=2sin(theta/2)=`second member.