InterviewSolution
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InterviewSolution
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solve`:sin^-1x+sin^-1 2x=pi/3` |
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Answer» `sin^(-1)x + sin^(-1)2 x = (pi)/(3)` `rArr " "sin^(1)x + sin^(1)2x = sin ^(1).(sqrt(3))/(2) sin^(-1)2x = sin^(1).sqrt(3)/(2) -sin^(-1)x` `" "=sin^(1)[(sqrt(3))/(2) sqrt(1-x^(2) )-xsqrt(1-((sqrt(3))/(2))^(2))]` `rArr" "2x = sqrt(3)/(2)sqrt(1-x^(2))-(x)/(2)` `rArr" "(5x)/(2) =(sqrt(3))/(2) sqrt(1-x^(2))` `" "5x = sqrt(3) sqrt(1-x^(2))` `25x^(2) = 3(1-x^(2))=3-3x^(2)` `rArr " "28x^(2) =3` `rArr " "x^(2) =(3)/(28)` ` rArr" "x = pm (sqrt(3))/(2sqrt(7))` but gives equation is not satisfied by `x= - sqrt(3)/(2sqrt(7))` Therefore `x=sqrt(3)/(2sqrt(7))` |
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