# How to solve trig equations?

##### 1 Answer

To solve a trig equation, the common approach is to transform it into one or many Basic Trig Equations. Solving trig equations, finally, results in solving basic trig equations.

There are 4 types of basic trig equations:

sin x = a , cos x = a ; tan x = a ; cot x = a

See trig books to know how to solve basic trig equations.

#### Explanation:

To order to transform a complex trig equation into many basic trig equations we use:

Trig identities, factoring, definitions and properties of trig functions ...

Example 1. Solve: f(x) = sin 2x - sin x = 0.

Use trig identity: sin 2x = sin x.cos x to transform.

f(x) = 2sin x.cos x - sin x = sin x(2cos x - 1) = 0

Example 2. Solve: sin 4x = cos 3x.

Use property of complementary arcs to transform:

a.

b.

Example 3. Solve:

Use trig identity: