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

If `(sin theta + cos theta )=sqrt(2) cos theta `, show that `cot theta =(sqrt(2)+1).`

Text Solution

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`sintheta+costheta=sqrt(2) costheta`
`rArr 1+cottheta=sqrt(2)cottheta " " [ "dividing both side by "sintheta]`
`rArr (sqrt(2)-1)cottheta=1 rArr cottheta=(1)/((sqrt(2)-1))=(1)/((sqrt(2)-1))xx((sqrt(2)+1))/((sqrt(2)+1))=(sqrt(2)+1)`
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