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If x in (0,pi/2), then show that cos^(-1...

If `x in (0,pi/2),` then show that `cos^(-1)(7/2(1+cos2x)+sqrt((sin^2x-48cos^2x))sinx)=x-cos^(-1)(7cosx)`

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If x in(0,(pi)/(2)), thenshowthat(d)/(dx)cos^(-1){(7)/(2)(1+cos2x)+(sqrt(sin^(2)x-48cos^(2)x))sin x}=1+(7sin x)/(sqrt(sin^(2)-48cos^(2)x))

If x in (0, (pi)/(2)) , then show that cos^(-1) ((7)/(2) (1 + cos 2 x) + sqrt((sin^(2) x - 48 cos^(2) x)) sin x) = x - cos^(-1) (7 cos x)

Knowledge Check

  • (d)/(dx)[(1+cos2x+sin2x)/(1+sin2x-cos2x)]=

    A
    `sec^(2)2x`
    B
    `2sec^(2)2x`
    C
    `-cosec^(2)x`
    D
    `4sec^(2)2x`

  • sqrt(cos 2x)+sqrt(1+sin2x)=2sqrt(sinx+cosx) if

    A
    `sin x+cosx=1 `
    B
    `x =2n pi `
    C
    `x=n pi+pi//4 `
    D
    `sin x -cosx=0`

  • If f(x)={sin^(-1)(sinx),xgt0 (pi)/(2),x=0,then cos^(-1)(cosx),xlt0

    A
    x=0is apoint of maxima
    B
    x=0 is a point of minima
    C
    x=0 is a point of intersectionn
    D
    none of these

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