Answer:
c.[tex]\frac{\pi}{2}[/tex]
Step-by-step explanation:
We are given that
[tex]y=sin(x-C)[/tex]
We have to find the value of C for which given function is even function.
We know that
Even function : If f(x)=f(-x) then the function is called even function.
[tex]a.2\pi[/tex]
Substitute the value then we get
[tex]y= sin(x-2\pi)= sin(-(2\pi-x))=-sin (2\pi-x)=sin x[/tex]
We know that sin (-x)=-sin x, [tex]sin(2\pi-x)=-sinx[/tex]
We know that Sin x is an odd function , therefore, option a is incorrect.
b.[tex]\pi[/tex]
Substitute the value then we get
[tex]y= sin (x-\pi)=sin(-(\pi-x))=-sin (\pi-x)=-sin x[/tex]
It is an odd function.
Hence, option b is incorrect.
c.[tex]\frac{\pi}{2}[/tex]
Substitute the value then we get
[tex]y= sin(x-\frac{\pi}{2})=sin(-(\frac{\pi}{2}-x))=-sin(\frac{\pi}{2}-x)=-cos x[/tex]
[tex] sin(\frac{\pi}{2}-x)=cosx [/tex]
We know that cos x is even function
Replace x by -x then, we get
[tex]-cos (-x)=-cos x[/tex]....(cos (-x)=cos x)
Hence, the value of C=[tex]\frac{\pi}{2}[/tex] for which given function will be an even function.
Answer:c.[tex]\frac{\pi}{2}[/tex]
