Solve that following equations : `sqrt(3)costheta`+ `sintheta=1`

Explanation

Given:
`sqrt3 costheta+sintheta=1`
Multiply `1/2`on both sides
`1/2sintheta+sqrt3/2costheta=1/2`
`sin(pi/6)sintheta+cos(pi/6)costheta=1/2`
`costhetacos(pi/6)+sinthetasin(pi/6)=1/2`
Using Identity
`cos(A-B)=cosAcosB+sinAsinB)`
`cos(theta-(pi/6))=1/2=cos(pi/3)`
General solution is`alpha=pi/3`
`theta=2npi pm alpha`, where `n in Z`
`theta-pi/6=2npi pm pi/3`
`theta=2npi pm pi/3+pi/6`
`theta=2npi +pi/6 pm pi/3`