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Solve the following for x: sin^−1(1−x)−2 sin^−1 x=π/2 - Mathematics

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Solve the following for x:

`sin^(-1)(1-x)-2sin^-1 x=pi/2`

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Solution

 

`sin^(-1)(1-x)-2sin^-1 x=pi/2`

`sin^(-1)(1-x)=pi/2+2sin^-1 x`

`=>(1-x)=sin(pi/2+sin^-1 x)`

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

`=>(1-x)=cos(cos^-1 (1-2x^2))`

`=>(1-x)=(1-2x^2)`

`=>2x^2-x=0`

`=>x=0, x=1/2`

Concept: Inverse Trigonometric Functions (Simplification and Examples)
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