Find the value of tan `75^(@)`.

Explanation

We have, `tan75^(@)=tan(45^(@)+30^(@))`
`(tan45^(@)+tan30^(@))/(1- tan45^(@)*tan30^(@))`
`=(1+(1)/(sqrt(3)))/(1-1xx(1)/(sqrt(3)))=(sqrt(3)+1)/(sqrt(3)-1)`
`((sqrt(3)+1)/(sqrt(3)-1))((sqrt(3)+1)/(sqrt(3)+1))=(3+1+2sqrt(3))/(2)=2+sqrt(3)`
`:. tan 75^(@)=(sqrt(3+1))/(sqrt(3-1)) or 2+sqrt(3)`.