The value of `alpha` such that `sin^(-1)(2/(sqrt(5))),sin^(-1)(3/(sqrt(10))),sin^(-1)alpha` are the angles of a triangle is

Options

A. `(-1)/(sqrt2)`
B. `(1)/(2)`
C. `(1)/(sqrt3)`
D. `(1)/(sqrt2)`

Answer

D

Explanation

According to the question
`sin^(-1).(2)/(sqrt5) + sin^(-1).(3)/(sqrt10) + sin^(-1) alpha = pi`
`rArr tan^(-1) 2 + tan^(-1) 3 + tan^(-1) ((alpha)/(sqrt(1 - alpha^(2)))) = pi`
`rArr pi + tan^(-1).(2+ 3)/(1 -(2) (3)) + tan^(-1) ((alpha)/(sqrt(1 - alpha^(2)))) = pi`
`rArr tan^(-1) ((alpha)/(sqrt(1 - alpha^(2)))) = (pi)/(4)`
`rArr (alpha)/(sqrt(1 - alpha^(2)) ) = 1`
`rArr alpha = (1)/(sqrt2)`