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If costheta+sintheta=sqrt2sintheta then ...

If `costheta+sintheta`=`sqrt2sintheta` then `sintheta-costheta` is

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`(costheta+sintheta)^(2)=2sin^(2)theta rArr cos^(2)theta+sin^(2)theta+2costhetasintheta=2 sin^(2)theta`
`rArr sin^(2)theta-2costhetasintheta= cos^(2)theta rArr sin^(2)theta - 2costhetasintheta+cos^(2)theta=2cos^(2)theta.`
`rArr (sintheta-costheta)^(2)=2cos^(2)theta rArr (sintheta- costheta )=sqrt(2) costheta.`
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