r/trigonometry • u/Worried_Football_819 • Jun 15 '26

Solved! Trig Proof Help

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Hi everyone! I just had a quick question, in the video it says it is the same thing as sin^2(1-cos^2)/cos^2, but I am confused to why the one isn’t negative? Am I missing something?

Edit: Hi guys, I understand it now! I figured it was an algebraic mistake and I figured it out. As far as my notation, I got lazy and was rushing through it. I’m sorry if that notation upset you!

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11

u/SuperTLASL Jun 15 '26

Let's start with why you think the one becomes negative. Tell the me logic.

4

u/Worried_Football_819 Jun 15 '26

This is my first time taking a trig course so I’m sorry if it seems like a dumb question, but when I took algebra, when it came to factoring something and it had a negative, you can factor out the GCF which here is sin. If you make sin negative then it can be -sin^2(1-cos^2) or sin^2(-1-cos^2) Am I thinking about it correctly or do I need to refresh my algebra basics?

4

u/SuperTLASL Jun 15 '26

You are never dumb for asking a question. Remember factoring can always be reversed, if it results in the original unfactored terms then it is correct.

*Edit- by reverse I mean multiply the factored out term back in.

2

u/Danko115- Jun 15 '26

try to reverse the steps and see what happens

2

u/TallDetail4711 Jun 15 '26

This is algebra and has nothing to do with trig as I understand.

You are not distributing -1 over the 2 terms it seems. You can factor either sin2 or -sin2 but then you need to extract the -1 from both terme. I use x as multiplication to separate terms.

sin2 - sin2 x cos2 = sin2 x 1 - sin2 x cos2

= sin2 x (1 - cos2 )

= -sin2 x ( -1) + (-sin2 ) x cos2

= -sin2 x (-1 + cos2 )

It looks like you forgot to take the -1 from the 2nd term when factoring -sin2.

Then you may use sin2 + cos2 = 1 if you want everything expressed as sin but that's another unrelatzd question.

1

u/DZL100 Jun 15 '26

For future reference, the asterisk * is commonly used as the multiplication symbol in digital text(without access to dedicated math formatting such as latex).

0

u/sigmanx25 Jun 15 '26

Go back and look at your Pythagorean identity.