`sin^(-1){sqrt((1-cosx)/(2))}`

intcot^(-1)sqrt((1+cosx)/(1-cosx))dx=

Prove that tan^(-1)(sqrt((1-cosx)/(1+cosx))=x/2, x lt pi .

Find the principal value of each of the following :(i)(sin^(-1)1)/(2)-2(sin^(-1)1)/(sqrt(2))( ii) sin^(-1){cos(sin^(-1)(sqrt((3)/(2)))}^(sqrt(2))

Find the differentiation of y=tan^(-1)sqrt((1+cosx/2)/(1-cosx/2))

Prove that : tan^(-1)((cosx)/(1-sinx))-cot^(-1)(sqrt((1+cosx)/(1-cosx)))=(pi)/(4), x in (0, pi//2) .

If int(cosx-sinx)/(sqrt(8-sin2x))dx=sin^(-1)((sinx+cosx)/(a))+C then a =

The sum of the infinte series sin^(-1)((1)/(sqrt(2)))+sin^(-1)((sqrt(2)-1)/(sqrt(6)))+...sin^(-1)((sqrt(n)-sqrt(n-1))/(sqrt(n(n+1))))

Differentiate sin^(-1){(sinx+cosx)/(sqrt(2))}, -(3pi)/4

y=sin^(-1)((sinx+cosx)/sqrt2)=?

If (sqrt(1+cosx)+sqrt(1-cosx))/(sqrt(1+cosx)-sqrt(1-cosx))=cot(a+x/2) and x in (pi,2pi) then 'a' is equal to :