Ta có :

`\int \frac{dy}{\sin y} = \ln | \tan(\frac{y}{2} ) | + C`

Biết : `\int_x^{\frac{\pi}{2}} \frac{dy}{\sin y} = [\ln | \tan (\frac{y}{2})|]_x^{\frac{\pi}{2}}`

`-> \ln | \tan ( \frac{\pi}{4} )| - \ln  \tan ( \frac{x}{2} ) |`

`= \ln(1) - \ln | \tan ( \frac{x}{2} ) |`

`= - \ln | \tan ( \frac{x}{2} ) |`

`= \ln | \cot ( \frac{x}{2})|`

`=>\int_x^{\frac{\pi}{2}} \frac{dy}{\sin y} = \ln[\cot( \frac{x}{2} )]`