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Find the value of cos^(-1)((x)/(2)+(sqrt...

Find the value of `cos^(-1)((x)/(2)+(sqrt(3-3x^(2)))/(2))`

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LHS`cos^(-1)x+cos^(-1){x/2+(sqrt3-3x^2)/2}`
`theta=cos^(-1)x`
`x=costheta`
`sintheta=sqrt(1-x^2)`
`cos^(-1)x+cos^(-1){cos(pi/3-theta)}`
`=cos^(-1)x+pi/3-theta`
`=cos^(-1)x+pi/3-cos^(-1)x`
`=pi/3=RHS`.
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