x" relative to "sin(cos(x^(2)))" Calculate "

" If determinant "|[cos^(2)x,sin^(2)x,cos^(2)x],[sin^(2)x,cos^(2)x,sin^(2)x],[cos^(2)x,sin^(2)x,-cos^(2)x]|" is expanded as a function of "sin^(2)x" ,then the absolute value of constant term in expansion of function "

int(sin^(2)x cos^(2)x)/((sin^(5)x+cos^(3)x sin^(2)x+sin^(3)x cos^(2)x+cos^(5)x)^(2))backslash dx

int(sin^(2)x cos^(2)x)/((sin^(5)x+cos^(3)x sin^(2)x+sin^(3)x cos^(2)x+cos^(5)x)^(2))backslash dx

The value of (2(sin2x+2cos^(2)x-1))/(cos x sin x cos3x+sin3x) is

If determinant |[cos^(2)x,sin^(2)x,cos^(2)x],[sin^(2)x,cos^(2)x,sin^(2)x],[cos^(2)x,sin^(2)x,-cos^(2)x]| is expanded as a function of sin^(2)x ,then the absolute value of constant term in expansion of function is

int( cos 2 x)/(sin x+cos x)^2 d x is equal to a) -1/(sin x+cos x)+C b) log |sin x+cos x|+C c) log |sin x-cos x|+C d) 1(sin x+cos x)^2

Prove that sin 3x + sin 2x - sin x = 4 sin x cos ""(x)/(2) cos "" ( 3x )/(2)

(i) int(cos^(3) x+ sin^(3) x)/(sin^(2) x.cos ^(2) x)dx " "(ii) int(cos2x)/(cos^(2) x sin^(2)x) dx

(i) int(cos^(3) x+ sin^(3) x)/(sin^(2) x.cos ^(2) x)dx " "(ii) int(cos2x)/(cos^(2) x sin^(2)x) dx