" (48)."cos^(-1)(2x-1)

2cos^(-1)x=cos^(-1)(2x^(2)-1)

cos^(-1){1/2x^(2)+sqrt(1-x^(2))sqrt(1-(x^(2))/(4))}=cos^(-1)((x)/(2))-cos^(-1)x holds for what values of x?

cos^(-1){1/2x^(2)+sqrt(1+x^(2))sqrt(1-x^(2))/(4)}=cos^(-1)(x)/(2)-cos^(-1)x

cos^(-1){1/2x^(2)+sqrt(1+x^(2))sqrt(1-x^(2))/(4)}=cos^(-1)(x/2)-cos^(-1)x

cos^(-1){1/2x^(2)+sqrt(1+x^(2))sqrt(1-x^(2))/(4)}=cos^(-1)(x)/(2)-cos^(-1)x

cos^(-1){1/2x^(2)+sqrt(1+x^(2))sqrt(1-x^(2))/(4)}=cos^(-1)(x/2)-cos^(-1)x

If x in (0,pi/2),t h e ns howt h a t d/(dx)cos^(-1){7/2(1+cos2x)+(sqrt(sin^2x-48cos^2x))sinx} =1+(7sinx)/sqrt(sin^2-48cos^2x)

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

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