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The number of values of x for which sin^...

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)/9….)=pi/2," where "0 le abs(x) lt sqrt(3)`, is

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Knowledge Check

  • If Sin^(-1)(x-x^(2)/2+x^(3)/4)+Cos^(-1)(x^(2)-x^(4)/2+x^(6)/4…..)=pi/2" for "0 lt abs(x) lt sqrt(2) then x =

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    B
    1
    C
    `-1//2`
    D
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  • The values of x for which (x-1)/(3x+4) lt (x-3)/(3x-2)

    A
    `(-oo, (5)/(4))`
    B
    `(-(4)/(3), (2)/(3))`
    C
    `((3)/(4), oo)`
    D
    `(-oo, -(5)/(4)) uu (3//4, oo)`

  • If sin^(-1)(x-(x^(2))/2+(x^(3))/4-……oo) +cos^(-1)(x^(2)-(x^(4))/2+(x^(6))/4-……..oo)=(pi)/2 and 0ltxltsqrt(2) then x=

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    `1/2`
    B
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    D
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    The number of roots o x in [0,2pi] for which |sqrt(2sin^(4)x+18cos^(2)x)-sqrt(2cos^(4)x+18sin^(2)x)|=1 is

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