If `y=cot^(-1)(sqrt(cos"x"))-tan^(-1)(sqrt(cos"x")),` prove that `siny=tan^2x/2`

If y=cot^(-1)(sqrt(cos x))-tan^(-1)(sqrt(cos x)), prove that sin y=tan^(2)(x)/(2)

If u = cot^(-1) sqrt(cos 2theta) - tan^(-1) sqrt(cos 2theta) prove that sin u = tan^(2) theta . .

cot_(sin x)^(-1)(sqrt(cos alpha))-tan^(-1)(sqrt(cos alpha))=x then

cot^(1) sqrt(cos alpha) -tan^(-1) sqrt(cos alpha)= x then sin x

If u= cot ^(-1) (sqrt(cos 2 theta)) -tan ^(-1)(sqrt(cos 2 theta)) , then prove that : sin u = tan^(2) theta .

If y=tan^(-1)sqrt((1-cos x)/(1+cos x)), prove that (dy)/(dx)=(1)/(2)

if cot^(-1)[sqrt(cos alpha)]-tan^(-1)[sqrt(cos alpha)]=x then sin x is equal to

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))