Solve the equation `sqrt3cos x + sin x = sqrt2 `.

Explanation

We have,
`sqrt(3) cos x + sin x=sqrt(2)` ...(1)
Dividing both sides by `sqrt((sqrt(3))^(2)+1^(2))=2`, we get
`sqrt(3)/2 cos x+1/2 sin x=1/sqrt(2)`
`rArr cos(x-pi/6)=1/sqrt(2)`
`rArr cos(x-pi/6)="cos" pi/4`
`rArr x-pi/6=2n pi pm pi/4, n in Z`
`rArr x= 2n pi pm pi/4+pi/6`
`rArr x=2npi +pi/4+pi/6 or x=2npi - pi/4+pi/6`
`rArr x=2n pi +(5 pi)/12 or x=2npi-pi/12`, where `n in Z`