Question

Solve that following equations : `"tantheta"+"tan"2"theta"+sqrt(3)"tanthetatan"2"theta"=""sqrt(3)`

Answer 1

`sintheta/costheta+(cos2theta)/cos2theta+sqrt3sintheta/costheta*(sin2theta)/cos2theta=sqrt3`
`(sinthetacos2theta+sin2thetacostheta+sqrt3sinthetasin2theta)/(costhetacos2theta)=sqrt3`
`sin(theta+2theta)+sqrt3(sinthetasin2theta-costhetacos2theta)=0`
`sin3theta-sqrt3(costhetacostheta-sinthetasin2theta)=0`
`sin3theta-sqrt3cos3theta=0`
`tan3theta=sqrt3`
`theta=pi/9`
General solution
`theta=pi/9pmnpi`.