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))))`

sin^(-1)(1/2)-2sin^(-1)(1/(sqrt(2)))

sin^(-1)sqrt(x)+cos^(-1)sqrt(1-x)=

sin^(-1)sqrt(x)+cos^(-1)sqrt(1-x)=

Find (dy)/(dx) if y=sec^(-1)((sqrt(x)+1)/(sqrt(x)-1))+sin^(-1)((sqrt(x)-1)/(sqrt(x)+1))

The sum of the series (1)/(sqrt(1)+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))+ . . . . .+(1)/(sqrt(n^(2)-1)+sqrt(n^(2))) equals

Sum the series to infinity : sqrt(2)- (1)/(sqrt(2))+(1)/(2(sqrt(2)))-(1)/(4sqrt(2))+ ....

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

If y = sec^(-1) (sqrt(x+1)/(sqrt(x-1)))+ sin^(-1)(sqrt(x-1)/(sqrt(x+1))) then (dy)/(dx) =

The sum of series sec^(-1)sqrt(2)+sec^(-1)(sqrt(10))/3+sec^(-1)(sqrt(50))/7++sec^(-1)sqrt(((n^2+1)(n^2-2n+2))/((n^2-n+1)^2)) is tan^(-1)1 (b) n tan^(-1)(n+1) (d) tan^(-1)(n-1)

Evaluate: int(sin^(-1)sqrt(x)-cos^(-1)sqrt(x))/(sin^(-1)sqrt(x)+cos^(-1)sqrt(x))\ dx