# Solve a Trig Equation by Finding a Greatest Common Factor

The trigonometry equations that require finding a greatest common factor, factoring it out, and then solving the equation could look like one of the following two equations:

Both of these equations are solved here.

Factor out sin

*x*from each of the two terms.Set the two different factors equal to 0.

Solve for the values of

*x*that satisfy both equations. Use a scientific calculator.All these values are solutions for the original equation. The complete list is

*x*= 0°, 60°, 180°, 300°.Move the term on the right to the left by subtracting it from each side.

A common error in algebra — which could carry over in trig — is to divide each side by the common factor. You should never do that, because you’ll lose part of the solution.

Factor out the cos

*x*from each term.You don’t want to divide each side by cos

*x*, because you’ll lose a solution if you do.Set the two different factors equal to 0.

Solve for the values of

*x*that satisfy both equations.So the solutions are all of the form

*x*= 90° + 180°*n*or*x*= 60° + 180°*n*.