The general solution of the trigonometric equation `sinx+cosx=1` is given by 1.x=2npi,n=0,+-1,+-2`.. 2. x=2npi+pi/2; n=0,+-1,+-2, dot` 3. x='npi'+(-1)^n (pi/4)-(pi/4) ,n=0,+-1,+-2, ` 4.`none of these`

Explanation

`sinx+cosx=1`

`sinx=1-cosx`

`1-sinx=sqrt(1-sin^2x)`

`(1-sinx)^2=(1-sin^2x)`

`1+sin^2x-2sinx=1-sin^2x`

`2sin^2x-2sinx=0`

`2sinx(sinx-1)=0`

`sinx=0`

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