" (a) "f_(H_(c))(d)/(dn)f(x_(n)(sin x-sin3x)/(sin^(2)x-cos^(2)x)=2sin x

Prove that: ,,(sin x-sin3x)/(sin^(2)x-cos^(2)x)=2sin x

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)

f'(sin^(2)x)lt f'(cos^(2)x) for x in

f'(sin^(2)x)lt f'(cos^(2)x) for x in

f'(sin^(2)x)lt f'(cos^(2)x) for x in

If quad f_(n)(x)=(sin x)/(cos3x)+(sin3x)/(cos3^(2)x)+(sin3^(2)x)/(cos3^(3)x)+....+(sin3^(n-1)x)/(cos3^(n)x) then f_(2)((pi)/(4))+f_(3)((pi)/(4))=

If f_(n)(x) = (sin x)/(cos3x)+(sin 3x)/(cos 3^(2)x) +(sin 3^(2)x)/(cos 3^(3)x) +....+ (sin 3^(n-1)x)/(cos 3^(n)x)"Then" f_(2) ((pi)/(4)) + f_(3) ((pi)/(4))=

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)?

Find maximum value of 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):}| .

f(x)=(sin^(2)x)e^(-2sin^(2)x)*max f(x)-min f(x) =