Question

Find the general solution of cos x +sin x =1.

Answer 1

cos x + sinx = 1

`cosx1/sqrt2+sinx1/sqrt2=1/sqrt2`

`cosxcospi/4+sinxsinpi/4=cospi/4`

`cos(x-pi/4)=cos(pi/4)`

`"by " cosy=cos alpha`

`y=2npi+-alpha`

`x-pi/4=2npi+-pi/4`

`x-pi/4=2npi+pi/4 or x-pi/4=2npi-pi/4`

`x=2npi+pi/2 or x=2npi`