" 12."(sin x-cos x)^(2)=1-sin2x

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)

int(cos x+sin x)/(cos x-sin x)(1-sin2x)dx

Prove that: (1+sin2x-cos2x)/(1+sin2x+cos2x)=tanx

Integrate the following: int{(5cos^(3)x+2sin^(3)x)/(2sin^(2)x*cos^(2)x)+sqrt(1+sin2x)+(1+2sin x)/(cos^(2)x)+(1-cos2x)/(1+cos2x)}dx

Let f(x)=((2sin x+sin2x)/(2cos x+sin2x)*(1-cos x)/(1-sin x));x in R Consider the following statements.

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

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):}| .

If int(sin^(8)x-cos^(8)x)/(1-2sin^(2)x cos^(2)x)dx=a sin2x+C then a=

int_0^(pi//4)(x^2(sin2x-cos2x))/((1+sin2x)cos^2x)dx

int_0^(pi//4)(x^2(sin2x-cos2x))/((1+sin2x)cos^2x)dx