Find the general solution of :
`cosx-sinx=-1`

Explanation

`cos x-sinx=1`
Dividing both sides by `sqrt(1^2+(-1)^2)=sqrt(2)`, we get,
`(1)/(sqrt(2))cos x-(1)/(sqrt(2))sinx=(1)/(sqrt(2))`
`therefore cos.(pi)/(4)cosx-sin.(pi)/(4)sinx=cos.(pi)/(4)`
`therefore cos(x+(pi)/(4))=cos.(pi)/(4)`
The general solution of `cos theta =cosalpha is theta=2 n pi +-alpha, n in Z`.
`therefore` the general solution of (1) is given by `x+(pi)/(4)=2 n pi +-(pi)/(4), n in Z`
Taking positive sign , we get , `x+(pi)/(4)=2 n pi +(pi)/(4), n in Z`
`therefore x=2n pi , n in Z`
Taking negative sign , we get, `x+(pi)/(4)=2n pi - (pi)/(4), n in Z`
`therefore x=2 n pi , n in Z`
`therefore` the required solution is `x=2 n pi , n in Z or x=2 n pi-(pi)/(2), in Z`.