Question

How do you simplify `\frac { 1+ \tan ( 2\theta - 45) } { 1- \tan ( 2\theta - 45) }`?

Answer 1

`\frac { 1+ \tan ( 2\theta - 45) } { 1- \tan ( 2\theta - 45) }`

`=\frac { tan(45)+ \tan ( 2\theta - 45) } { 1- tan(45)\tan ( 2\theta - 45) }`

`=tan(45+2theta-45)=tan2theta`