Using the Angle Sum Formulae to Solve Trigonometric Equations

To solve an equation of the form

1. Expand both sides using the angle sum formulae:

(1)

(2)

(3)

(4)

2. Divide through byto obtain terms in

3. Transfer the terms into one side.will now be a common factor. Factorise with

3. Makethe subject andboth sides.

Example: Solve

The problem becomes

Divide byto obtain

Rearrange to give

Factorise with

Make tan x the subject:and arctan to give