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sin^(- 1)x=cos^(- 1)sqrt(1-x^2)...

`sin^(- 1)x=cos^(- 1)sqrt(1-x^2)`

Answer

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sin^(- 1)x+sin^(- 1)y=cos^(- 1) (sqrt(1-x^2) sqrt(1-y^2)-xy) if x in [0,1], y in [0,1]

sin^(-1)x+sin^(-1)y=cos^(-1)(sqrt(1-x^(2))sqrt(1-y^(2))-xy) if x in[0,1],y in[0,1]

Knowledge Check

  • If y=sin^(-1)x,z=cos^(-1)sqrt(1-x^(2))," then: "(dy)/(dz)=

    A
    `(1)/(sqrt(1-x^(2)))`
    B
    `cos^(-1)x`
    C
    1
    D
    `tan^(-1)((x)/(sqrt1-x^(2)))`

  • If x takes negative permissible values , then sin^(-1) x= a) cos^(-1)sqrt(1-x^2) b) -cos^(-1)sqrt(1-x^2) c) cos^(-1)sqrt(x^2-1) d) pi-cos^(-1)sqrt(1-x^2)

    A
    `cos^(-1)sqrt(1-x^2)`
    B
    `-cos^(-1)sqrt(1-x^2)`
    C
    `cos^(-1)sqrt(x^2-1)`
    D
    `pi-cos^(-1)sqrt(1-x^2)`

    • Similar Questions

    Explore conceptually related problems

    sin^(-1)x+sin^(-1)y=cos^(-1)""{sqrt((1-x^(2))(1-y^(2)))-xy}

    Prove the following: sin^-1x = cos^-1(sqrt(1-x^2))

    (d(sin^(-1)x))/(d(cos^(-1)sqrt(1-x^(2))))=?

    sin^(-1)sqrt(x)+cos^(-1)sqrt(1-x)=

    sin^(-1)sqrt(x)+cos^(-1)sqrt(1-x)=

    STATEMENT-1 : If tan^2 (sin^-1x) > 1 then x in(-1-1/sqrt2)uu(1/sqrt(2).1).STATEMENT-2 : The number of positive integral solution of tan^-1 1/y+cot^-1(1/x)=cot^-1(1/3), where x/y < 1, is 2. STATEMENT -3 : If sin^-1 x=-cos^-1 sqrt(1-x^2) and sin^-1 y=cos^-1 sqrt(1-y^2), then the exact range of (tan^-1 x+ tan6-1 y) is [-pi/4,pi/4].

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