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|

Explanation

`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`

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