(sinx-xcosx)/(xsinx+cosx)
.
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.
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