If `f(x)` is a real-valued function defined as `f(x)=In (1-sinx),` then the graph of `f(x)` is

Options

A. symmetric about the line `x =pi`
B. symmetric about the y-axis
C. symmetric and the line ` x=(pi)/(2)`
D. symmetric about the origin

Answer

C

Explanation

`f((pi)/(2)-x)=In (1-cos x)`
` and f((pi)/(2)+x)=In(1-cosx)`
Thus, `f((pi)/(2)+x)=f((pi)/(2)-x)`
Thus f(x) is symmetrical about line `x=(pi)/(2).`