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sin^(-1)(1-x)-2sin^(-1)x=pi/2, then x is...

`sin^(-1)(1-x)-2sin^(-1)x=pi/2`, then `x` is equal to (A) `0,1/2` (B) `1,1/2` (C) 0 (D) `1/2`

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To solve the equation \( \sin^{-1}(1-x) - 2\sin^{-1}(x) = \frac{\pi}{2} \), we will follow these steps: ### Step 1: Rearranging the Equation We start by rearranging the equation: \[ \sin^{-1}(1-x) = \frac{\pi}{2} + 2\sin^{-1}(x) \] ...
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Knowledge Check

  • If sin^(-1) (1-x)-2 sin^(-1) x= pi//2 , then x equals

    A
    `{0,-1//2}`
    B
    `{1//2,0}`
    C
    `{0}`
    D
    `{-1,0}`

  • If sin^(-1)xcot^(-1)(1/2)=(pi)/2 then x is equal to

    A
    `0`
    B
    `1/(sqrt(5))`
    C
    `2/(sqrt(5))`
    D
    `(sqrt(3))/2`

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