find the value

Question

tan(2Π/5)-tan(Π/15)-3½tan(2Π/5)tan(Π/15)

Answer 1

It's 3^1/2 (or √3), not 3½, correct?

 

tan(π/3) = tan (5π/15) 

 

            = tan(6π/15 - π/15)

 

            = tan(2π/5 - π/15)

 

            = [tan(2π/5) - tan(π/15)]/[1+ tan(2π/5)tan(π/15)]

 

So, √3 + √3tan(2π/5)tan(π/15)= tan(2π/5) - tan(π/15)

 

Therefore, tan(2π/5) - tan(π/15) - √3tan(2π/5)tan(π/15) = √3 

 

Answer 2

These angles are not on the unit circle.  Just use the calculator.