Trig identities to memorize:
I’ll go over some tips to help make proving trig identities a little easier, and then we will go through an example step by step, so you can understand the thought process when proving trig identities.
- Don’t work on both sides of the equation at the same time
- Start on the more complicated side
- Try converting everything into cosine and sine
- Try working on the other side if you get stuck
- Memorize the identities
- If you get frustrated, take a break and look at it again with fresh eyes
Let’s give one a try . . . (click here):
1. We will start on the more complicated side (right side) and convert everything to sine and cosine.
2. It looks a little messy, so let’s simplify it.
3. I’m stumped as to what to do next, so we’ll start working on the left side and convert everything to sine and cosine.
4. This looks familiar. Let’s use the double angle identities. We know what identity to use for cos(2x) based on what the right side of the equation looks like.
5. The left side now matches the right side. We’re done!
Proving trig identities take a lot of practice. Let’s look at two more examples.
Here’s an example (click here):
Last example (click here):
Proving trig identities can be very tricky. It is important to not give up, if you are stumped. Take a break and come back to the problem. Have a page of the identities out in front of you, so you can see your options. The only way to get better is to practice proving trig identities. Check out Symbolab’s trigonometry practice for more help on the topic.
Until next time,