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|

Answer

3

Explanation

`sin^(-1) (x^(2) -- (x^(4))/(3) + (x^(6))/(9) -...) + cos^(-1) (x^(4) -(x^(8))/(3) + (x^(12))/(9) ...) = (pi)/(2)`
`rArr (x^(2) - (x^(4))/(3) + (x^(6))/(9)..) = (x^(4) - (x^(8))/(3) + (x^(12))/(9)...)`
or `(x^(2))/(1 + (x^(2))/(3)) = (x^(4))/(1 + (x^(4))/(3))`
or `(3)/(3 + x^(2)) = (3x^(2))/(3 + x^(4)) " or "x = 0`
or `9 + 3x^(4) = 9x^(2) + 3x^(4) " or " x = 0`
or `x^(2) = 1 rArr x = 0, 1 " or " -1`