Correct Answer - `a to q; b to q; c to s; d to p`
a. `f(x+pi//2)=cos(|sin(x+pi//2)|-|cos(x+pi//2)|)`
`=cos (|cosx|-|-sinx|)`
`=cos(|cosx|-|sinx|)`
`=cos(|sin x|-|cosx|)`
`=f(x)`
b. `f(x+pi//2)=cos[tan(x+pi//2)+cot(x+pi//2)].`
`cos[tan(x+pi//2)-cot(x+pi//2)]`
`=cos[-cotx-tanx]*cos[-cotx+tanx]`
`=cos(tanx+cotx)*cos(tanx-cotx)`
`=f(x)`
c. The period of `sin^(-1)(sinx) " is " 2pi.` The period of `e^(tanx) " is " pi`.
Thus, the period of `f(x)" is " LCM (2pi,pi)=2pi.`
d. The given function is
`f(x)=sin^(3)x sin 3x`
`=((3sinx-sin 3x)/(4)) sin 3x`
`=(3)/(8) (cos 2x-cos 4x)-(1)/(8)(1-cos6x)`
Thus, the period of `f(x) " is " pi.`