Question

How do you simplify 1/(cos(x/2)sin(x/2)) to 2cosec(x) ?

Answer 1

Use \[\sin(2\theta)=2\sin \theta \cos \theta\]

Answer 2

\[\theta=x/2\]

Answer 3

\[\frac{1}{\text{Cos}\left[\frac{x}{2}\right]\text{Sin}\left[\frac{x}{2}\right]}=\frac{1}{\left(\frac{\text{Sin}[x]}{2}\right)}=2 \text{Csc}[x] \]

Answer 4

\[\frac{1}{\text{Cos}\left[\frac{x}{2}\right]\text{Sin}\left[\frac{x}{2}\right]}=\frac{1}{\left(\frac{\text{Sin}[x]}{2}\right)}=2 \text{Csc}[x] \]