f(x)=(sin12x)/(1+cos^(2)6x)

Find the period of the functions (where [ * ] denotes greatest integer function) f(x) = (sin 12 x )/(2cos^(2) 6x-1)

f_(1)(x)=sin^(-1)(cos(sin^(2)x)),f_(2)(x)=cos^(-1)(sin(cos^(2)x)),f_(3)(x)=sin^(-1)(cos^(2)x)),f_(4)(x)=cos^(-1)(sin^(2)x)* Then which of the following is/are correct?

Let (d)/(dx)(f(x))=((sin^(12)x-cos^(12)x)/((sin^(2)x-cos^(2)x)(1-3sin^(2)x cos^(2)x))) be such that f(0)=0 then f((pi)/(2)) equals (k pi)/(16). Find the value of k(k in N)

If f(x)=|(sin^(2)x, cos^(2)x,1),(cos^(2)x,sin^(2)x,1),(-10,12,2)| , then intf(x)dx=

If f(x)=|(1+sin^(2)x,cos^(2)x,4sin2x),(sin^(2)x,1+cos^(2)x,4sin2x),(sin^(2)x,cos^(2)x,1+4sin2x)| then the maximum value of f(x) is

If f(x)=det[[sin^(2)x,cos^(2)x,1cos^(2)x,sin^(2)x,1x-12,12,2]] then f'((pi)/(2))=

If f(x) = |(1+sin^(2)x,cos^(2)x,4 sin 2x),(sin^(2)x,1+cos^(2)x,4 sin 2x),(sin^(2)x,cos^(2)x,1+4 sin 2x)| What is the maximum value of f(x)?

If f(x)="sin"^(-1)((1-"cos"2x)/(2"sin"x)) , then |f'(x)| is equal t o