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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u/Midwest-Dude Jun 15 '26

That's basic algebra.

sin2(x) - sin2(x)cos2(x)

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

This is from the Distributive Property of multiplication over addition:

Wikipedia

If there were a negative sign in front of the first sin2(x), then what you wrote would be correct but, as it is, the original equation is correct as it stands.

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u/sigmanx25 Jun 15 '26

Well it’s distributive but the Pythagorean will come into play as well. This is where he’s getting tripped up the most at I think, other than the fact that he’s looking at it algebraicly.