Here we would like to solve the following equation for



- We can change into



- We can get a common denominator of and factor it out.



-From here we change the $\2cos^2 \theta $ into using our useful Pythagorean identity. Also, we move it to switch places with the in the same step.





-Simplifying within parentheses gives :





-Now we have an expression that's factorable. So we factor it!





-We now have three factors that we can set equal to zero.



Solving gives . Between 0 and 360 degrees, 90 and 270 are the only ones that work.

Solving gives . Between 0 and 360 degrees, 210 and 330 are the solutions.

Solving gives . Obviously, there are no real solutions for in this case.


However, we have to double-check our solutions degrees. We have to check because when we got a common denominator of , we introduced a variable.


Substituting our solutions into the original equations results in this [used radians because don't know how to do degree symbol] :



That obviously didn't work.
Since I have to go soon, we also know then from that^^ that 180 [pi radians] does not work either.

So our final solutions are and [degrees].