No specific question as to what is to be done with the above ratio.
To find the value of the expression as a ratio, we need to put x=some angle and evaluate the ratio.
The expression is already in a form and does not require any simplification.
The limit of the expression at pi/2 is 2/pi
The limit of the expression when x=0, is zero clearly.
You can ask for any further help related with this.