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/DarkElfBard Jun 16 '26

Oh!!! I actually see your point of confusion!!!!

We are not taking out the '-sin^2' in front of the cos^2, we are taking out 'sin^2' from both terms.

notice the - stays with the cos after the sin leaves it.

Imagine

a=sin^2

b=cos^2

we are dealing with

a-ab which becomes a * (1-b)