Now that we have become comfortable with the steps for verifying trigonometric identities it’s time to start Proving Trig Identities!
Let’s quickly recap the major steps and ideas that we discovered in our previous lesson.
Can we plug in values for the angles to show that the left hand side of the equation equals the right hand side?
Sadly, no. There are an infinite number of coterminal angles that could make a trig equation true, and sometimes one angle can prove true where others would not. So as Purplemath says, “let’s don’t do that.”
Can we move terms from one side to the other? or work on both sides?
Again, the answer is no. We must pick one side to work on (HINT: pick the side that looks “nasty” and complicated because it give you more to work with), and use our knowledge of our fundamental identities to transform it to look like the other.
Do we have to write down theorems of reasons for each manipulation?
Nope! Just show all your steps!
Step-by-Step Example of Proving Trig Identities
Will this be hard?
Not all trigonometric identities are created equal. Some are easy and obvious, while other will take time and some savviness.
The trick to being successful is to not give up!
You have the tools and tricks to help you to get to the answer, you just need to practice and persevere.
In this lesson we will continuously review the fundamental identities and the steps we learned previously for proving trig identities in order to tackle 15 classic examples that will give you all the skills necessary to handling even the hardest problem.
How to Prove Trig Identities – Video
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