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 `(-1)/(sqrt(2))` (b) `1/2` (c) `1/(sqrt(3))` (d) `1/(sqrt(2))`

Explanation

`sin^-1(2/sqrt5) = tan^-1 2`

`sin^-1(3/sqrt10) = tan^-1 3`

`sin^-1(alpha) = tan^-1 (alpha/(sqrt(1-alpha^2)))`

So, given equation becomes,

`tan^-1 2 + tan^-1 3 + tan^-1 (alpha/(sqrt(1-alpha^2))) = pi`

As `2*3 >1`,

`:. tan^-1 2 + tan^-1 3 = pi +tan^-1((2+3)/(1-(2)(3))) = pi+tan^-1(-1) `

So,our equation becomes,

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