This question can be found in Heffernan's 2007 exam 1 for Maths Methods:

Solve over the domain [0,2*pi]:

tan2(x) + (1-rt(3))tan(x) = rt(3)

My working:

Let tan(x) = A

A2 + (1-rt(3))A = rt(3)

A2 + [(rt(3)/rt(3)) - (rt(3)/1)]A - rt(3) = 0

A2 + [(rt(3)-3rt(3))/rt(3)]A - rt(3) = 0

And that's where I become lost, did I simplify the cofactor 'A' correctly? How would I complete this square? Once I have completed this square, how would I solve the equation?

Cheers!

## Solving Trigonometric Quadratic Equations

Answered## 1 Answer