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Putting `x =theta -pi/4` prove that `lim_(theta->pi/4)(sin theta - cos theta)/(theta -pi/4)=sqrt(2)`

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Putting `x =theta -pi/4` prove that `lim_(theta->pi/4)(sin theta - cos theta)/(theta -pi/4)=sqrt(2)`
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`x = theta - pi/4 => theta = x+pi/4`
So, given limit becomes,
`L.H.S. = Lim_(x->0) (sin(x+pi/4) - cos(x+pi/4))/x`
`= Lim_(x->0) ((sinx1/sqrt2+cosx1/sqrt2) - (cosx1/sqrt2 - sinx1/sqrt2))/x`
`= Lim_(x->0) 2*1/sqrt2 sinx/x`
`=sqrt2**1 = sqrt2 = R.H.S.`
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