Proving the Double and Half Angle Formulas for Trigonometry (Precalculus - Trigonometry 27)

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Mr. Leonard! I am a former student from your Calc 2 class at MJC! Hope all is well! I finished my engineering degree and I’m so thankful to have participated in your lectures.

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Professor, I'm not really sure if you'll read this but I thought I needed to leave this comment here either way. Around 2 years ago, I found a field I'm really passionate about, but I unfortunately did not have the mathematical chops to deal with its rigor. Math was always a subject that I was terrified of thinking I'm not smart enough to succeed in, but to be honest, that was 100% down to bad teaching methods and me not putting enough work in. Fast forward those 2 years, having gone through all your playlists from pre-algebra to Calc 3, I've passed all my foundational classes with straight A's, and I'm now at a well-respected university doing the degree I've always wanted to do. Even though you've never taught me in person, I can't stress on the impact you've had on my academic career so far. You are a truly phenomenal teacher, and I sincerely hope your students appreciate how lucky they are to have you. I don't really know what to say at this point other than thank you! Keep being awesome!

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[@georgesadler7830]

Professor Leonard ,thank you for another tremendous video/lecture on Proving the Double and Half Angle Formulas in Trigonometry/Precalculus. I used these well known formulas in Calculus and Electrical Engineering courses in years past and they are very useful in solving complex problems. Proving formulas and concepts in Mathematics are also important.

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I know I am a little late, but congrats on surpassing half a million subscribers! Your calculus videos got me through my first two years of math, and I want to you know that I am really grateful for that. Wishing you and your family all the best professor Leonard! Stay safe and God bless.

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Thank you for this. I need to learn these to help with calculus.

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In 1 year, I'll be sure to come back to this video after mastering the other lower level mathematics. xD

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...

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