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

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))

Principal value of sin^(-1)(1)+sin^(-1)((1)/(sqrt2)) is

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))))

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)/(sqrt (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))))

sin^(-1)((1)/(sqrt(2)))-3sin^(-1)((sqrt(3))/(2))=

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