A continuous, even periodic function f with period 8 is such that `f(0)=0,f(1)=-2,f(2)=1,f(3)=2,f(4)=3,` then the value of `tan^(-1) tan{f(-5)+f(20)+cos^(-1)(f(-10))+f(17)}` is equal to

Options

A. `2pi-3`
B. `3-2pi`
C. `2pi+3`
D. `3-pi`

Answer

D

Explanation

`f(-5)=f(3)=2,f(20)=f(4)=3,f(-10)=f(-2)=f(2)=1`,
`f(17)=f(1)=-2`
`therefore" "tan^(-1)tan{f(-5)+f(20)+cos^(-1)(f(-10))+f(17)}`
`" "=tan^(-1)tan(2+3+0-2)=3-pi`.