Question

Use inverse functions where needed to find all solutions of the equation in the interval (0,2pi)

Answer 1

Step 1 :

The trigonometric equation is and the interval is .

Factorize the trigonometric equation.

Since the range of the inverse tangent function is , obtain two solutions in the interval .

Step 2 :

The general solution of is , where is an integer.

The general solutions are , where is an integer.

Step 3 :

If , then

,

If , then

,

If , then

The solutions are , , and in the interval .

Solution :

The solutions are , , and in the interval .