# What are other methods for solving equations that can be adapted to solving trigonometric equations?

##### 1 Answer

**Solving concept.** To solve a trig equation, transform it into one, or many, basic trig equations. Solving a trig equation, finally, results in solving various basic trig equations.

There are 4 main basic trig equations:

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

Exp. Solve sin 2x - 2sin x = 0

Solution. Transform the equation into 2 basic trig equations:

2sin x.cos x - 2sin x = 0

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

Next, solve the 2 basic equations: sin x = 0, and cos x = 1.

Transformation process.

There are 2 main approaches to solve a trig function F(x).

1. Transform F(x) into a product of many basic trig functions.

Exp. Solve F(x) = cos x + cos 2x + cos 3x = 0.

Solution. Use trig identity to transform (cos x + cos 3x):

F(x) = 2cos 2x.cos x + cos 2x = cos 2x(2cos x + 1 ) = 0.

Next, solve the 2 basic trig equations.

2. Transform a trig equation F(x) that has many trig functions as variable, into a equation that has only one variable. The common variables to be chosen are: cos x, sin x, tan x, and tan (x/2)

Exp Solve

Solution. Call cos x = t, we get

Next, solve this equation for t.**
**Note

**. There are complicated trig equations that require special transformations.**