solve the multiple-angle equation

Question

(a) Equation :

Answer 1

The equation is .

Let , the function has a period of , first find all solutions in the interval .

The function is negative in third and fourth quadrant.

So the solutions are ; and substitute in .

        (In third quadrant)    (Substitute )

      (In fourth quadrant)   (Substitute )

Finally, add multiples of to each of these solutions to get the general form

where n is integer.

                    (Substitute )

                             (Divide each side by 2)

The solutions are .