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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))` |
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Answer» `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, `pi+tan^-1(-1) + tan^-1 (alpha/(sqrt(1-alpha^2))) = pi` `=>tan^-1 (alpha/(sqrt(1-alpha^2))) = tan^-1(1)` `=> alpha/(sqrt(1-alpha^2))= 1` `=>alpha^2 = 1-alpha^2` `=>alpha = 1/sqrt2` So, option `d` is the correct option. |
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