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Find the smallest positive root of the e...

Find the smallest positive root of the equation `sqrt(sin(1-x))=sqrt(cos"x")`

Text Solution

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The given equation is possible if `sin(1-x) ge 0` and `cos x ge 0`. On squaring, we get `sin(1-x)=cos x`
or `cos (pi/2-(1-x))=cos x`
`rArr pi/2-1+x=2npi pm x, n in Z`
or `x=(2npi-pi/2+1)/2, n in Z`
For `n=2, x=(7pi)/4+1/2`, which is the smallest positive root of the given equation.
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