Question 4 - A-Level Maths

Exam Board	CAIE
Module	P3 (Pure Mathematics 3)
Year	2011
Session	June
Topic	Addition & Double Angle Formulae

Show that the equation $$\tan \left( 60 ^ { \circ } + \theta \right) + \tan \left( 60 ^ { \circ } - \theta \right) = k$$ can be written in the form $$( 2 \sqrt { } 3 ) \left( 1 + \tan ^ { 2 } \theta \right) = k \left( 1 - 3 \tan ^ { 2 } \theta \right)$$
Hence solve the equation $$\tan \left( 60 ^ { \circ } + \theta \right) + \tan \left( 60 ^ { \circ } - \theta \right) = 3 \sqrt { } 3$$ giving all solutions in the interval $0 ^ { \circ } \leqslant \theta \leqslant 180 ^ { \circ }$.