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If cos theta+sin theta = sqrt(2) cos the...

If `cos theta+sin theta = sqrt(2) cos theta`, prove that `cos theta - sin theta = sqrt(2) sin theta`

Text Solution

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`costheta+sinntheta=sqrt2costheta`
`sintheta=sqrt2costheta=costheta`
`sintheta=costheta(sqrt2-1)`
`sintheta/(sqrt2-1)=costheta`
muliplying and dividing by `sqrt2+1`
`(sintheta(sqrt2+1))/(2-1)=costheta`
`(sqrt2+1)sintheta=costheta`
`sqrt2sintheta+sintheta=costheta`
...
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