Q.29 Find the sum of the series `sin^(-1)(1/sqrt(5))+sin^(-1)(1/sqrt(65))...`

Find 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/sqrt5)+cos^(-1)(3/sqrt(10))

Prove that: i) sin^(-1)(1/sqrt(5))+sin^(-1)(2/sqrt(5))=pi/2

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))))

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))))

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))))

cot (sin ^(-1)""(1)/(sqrt(5))+sin ^(-1)""(2)/(sqrt(5)))

sin^(-1)((1)/(sqrt(5)))+sin^(-1)((1)/(sqrt(10)))=(pi)/(4)

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))))

Find the sum of infinite series : S = sin^-1(1/sqrt2) + sin^-1((sqrt2 -1)/sqrt6) + sin^-1((sqrt3 - sqrt2)/sqrt12) + ...... infty