If `x in (0,pi/2),` then show that `cos^(-1)(7/2(1+cos2x)+sqrt((sin^2x-48cos^2x))sinx)=x-cos^(-1)(7cosx)`

If x in(0,(pi)/(2)), thenshowthat(d)/(dx)cos^(-1){(7)/(2)(1+cos2x)+(sqrt(sin^(2)x-48cos^(2)x))sin x}=1+(7sin x)/(sqrt(sin^(2)-48cos^(2)x))

If x in (0, (pi)/(2)) , then show that cos^(-1) ((7)/(2) (1 + cos 2 x) + sqrt((sin^(2) x - 48 cos^(2) x)) sin x) = x - cos^(-1) (7 cos x)

sqrt(2)cos^(2)7x-cos7x=0

(d)/(dx)[(1+cos2x+sin2x)/(1+sin2x-cos2x)]=

int_(0)^( pi/4)(x^(2)(sin2x-cos2x))/((1+sin2x)cos^(2)x)dx

(1+sin x+cos x+sin2x+cos2x)/(tan2x)=0

If f(x)={sin^(-1)(sinx),xgt0 (pi)/(2),x=0,then cos^(-1)(cosx),xlt0

The domain of the function f(x)=sqrt(abs(sin^(-1)(sinx))-cos^(-1)(cosx)) in [0,2pi] is

cos6x=32cos^(6)x-48cos^(4)x-18cos^(2)x-1