InterviewSolution
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InterviewSolution
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The number of values of `x`for which `sin^(-1)(x^2-(x^4)/3+(x^6)/9)+cos^(-1)(x^4-(x^8)/3+(x^(12))/9ddot)=pi/2,`where `0lt=|x| |
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Answer» `sin^-1(x^2-x^4/3+x^6/9+...)+cos^-1(x^4-x^8/3+x^12/9+...) = pi/2` We know, `sin^-1y+cos^-1y = pi/2` It means, `x^2-x^4/3+x^6/9+... =x^4-x^8/3+x^12/9+...` these are two G.P.s with common ratio `-x^2/3 and -x^4/3.` `x^2/(1+x^2/3) = x^4/(1+x^4/3)->(1)` `=>3/(3+x^2) = (3x^2)/(3+x^4)` `=>9+3x^4 = 9x^2+3x^4` `=>x = +-1` `x = 0` also is a solution for `(1)`. So there are `3` solutions available for the given equation. |
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