Period of `e^(cos^4 pix+x-[x])`

Period of e^(cos^(4)pi x+x-[x])

{.} denotes the fractional part function and [.] denotes the greatest integer function: Column I: Function, Column II: Period f(x)=e^cos^4pix+x-[x]+cos^(2pix) , p. 1//3 f(x)=cos2pi{2x}+sin2pi{2x} , q. 1//4 f(x)=sin3pi{x}+tanpi[x] , r. 1//2 f(x)=3x-[3x+a]-b ,w h e r ea , b , in R^+ , s. 1

{.} denotes the fractional part function and [.] denotes the greatest integer function: Column I: Function, Column II: Period f(x)=e^cos^4pix+x-[x]+cos^(2pix) , p. 1//3 f(x)=cos2pi{2x}+sin2pi{2x} , q. 1//4 f(x)=sin3pi{x}+tanpi[x] , r. 1//2 f(x)=3x-[3x+a]-b ,w h e r ea , b , in R^+ , s. 1

The period of cos4x is

Find the period of cos^(2) x+ cos^(4) x

Find the periods of following functions. {:((i)f(x)=[sin3x]+abs(cos6x),(ii)f(x)=1/2{abs(sinx)/cosx+abs(cosx)/sinx}),((iii)f(x)=e^(cos^(4)pix+x-[x]+cos^(2)pix),(iv)f(x)=3sin""(pix)/3+4cos""(pix)/4):} {:((v)f(x)=cos3x+sinsqrt(3)pix,(vi)f(x)=sin""(pix)/(n!)-cos(pix)/((n+1)!)),((vii)f(x)=x-[x-b],(viii)f(x)=e^(In(sinx))+tan^(3)x-cosec(3x-5)):}

period of cos"" (pix)/(4) - 2 cosec (pix)/( 6) + 5 tan"" (pix)/(3) is

Statement - I : Period of cos^(3) x + cos^(3) (120^(0) - x) + cos^(3) (120^(0) + x ) is (pi)/(3) Statement -II : Period of cos((2pi x)/ 3 ) + sin((pix)/2) - tan ((pi x )/ 4) is 12 Which of the above statement is correct.

The period of sin^4 x + cos^(4) x is