Squaring Trigonometric Functions

Squaring Trigonometric Functions- Emily Smith

In class today we learned about squaring trigonometric functions. This is another way to help people solve identities. When two different trigonometry functions are on either side of the equation and you cannot use a Pythagorean identity, you cannot factor, and changing it into sin and cos doesn’t help, you must square both sides of the equation.

Example:
cosx+1= sinx <-- you cannot use a Pythagorean identity or factor so you must square both sides
(cosx+1)2=(sinx)2
(cosx+1)(cosx+1)=sin2x
cos2x+cosx+cosx+1=sin2x
cos2x+2cosx+1=sin2x
cos2x+2cosx+1=1-cos2x
+cos2x +cos2x
________________________
2cos2x+2cosx+1=1
-1 -1
________________________
2cos2x+2cosx=0
2cosx(cosx+1)=0

2cosx=0
x=π/2,3π/2

cosx+1=0
-1 -1
x=π

***** Because you squared the equation you must check for extraneous solutions. You must plug π/2,3π/2, and π in for x and make sure that the equations are equal.
In this problem when you plug the solutions in for x 3π/2 does not work.
There are two times that you must check for extraneous solutions…
1. Squaring equations
2. Fractions such as tan where it is sin/cos