" 7."cot^(-1)(sqrt((1+cos3x)/(1-cos3x)))

tan ^(-1)(sqrt((1-cos 3 x)/(1+cos 3x)))

prove that cot^(-1)[sqrt((1+cos3x)/(1-cos3x))]

tan ^(-1)(sqrt((1-cos 3 x)/(1+cos x)))

intsqrt((1+cos 3x)/(1-cos3x))dx=

prove that tan^(-1)((cos x)/(1-sin x))-cot^(-1)((sqrt(1+cos x))/(sqrt(1-cos x)))=(pi)/(4),x varepsilon(0,(pi)/(2))

If y=cos^(-1)sqrt((cos3x)/(cos^3x)),then show (dy)/(dx)=sqrt(3/(cosxcos3x))

y=cos^(-1)sqrt((cos3x)/(cos^(3)x)), thenshowthat (dy)/(dx)=sqrt((3)/(cos x cos3x))

Simplest form of tan^(-1)((sqrt(1+cos x)+sqrt(1-cos x))/(sqrt(1+cos x)-sqrt(1-cos x))), pi lt x lt (3 pi)/(2) is: