The Double-Angle Formulas | proof without words| mathocube|

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In this video, we are going to find the visual proof the Double-Angle Formulas.
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[@redangrybird7564]

I appreciate all the time you've dedicated to make this video, thanks.
I was curious about the proof but this is superb. 😷👍

[@Mathocube]

Glad you liked it!

[@erinhopper6568]

Thank you, this was beautiful!!

[@andrewsansom9721]

This is a beautiful proof. Thank you for sharing!

[@gocrazy432]

Thanks, this was really healpful. I might link this in low budget trig/geometry proof I'm working on. Would you mind?

[@somehow49]

You are an angel

[@Mathocube]

🤗

[@mxnry1147]

Thank you!

[@soragya1204]

Thanks i always messed up with formulas 😅😊

[@CompCode-Central]

amazing stuff

[@jorgebejarano1783]

Excelente, Felicitaciones👍👍🏽

[@himaniranga3140]

🤔Trigonometry 😁👍

[@Mathocube]

Yes mam it's trigonometry

[@ultrio325]

Turns out all I missed was a theorem!

[@bijoymandal9543]

You are a mathematician

[@manarsalem1685]

why is AP and BP equal to cosine theta?

[@PujaKaul-y1t]

But if we value it's not proof please help

[@prasadguy]

Can anyone tell me how
BC = AB.cos theta
AC = AB.sin theta
Are true?

[@adamex2270]

This pleases the nut

[@cariogenic]

I had an investigation where you had to prove the double angle rules with this method. I was only able to prove the sin one sadly

[@kingrobert7246]

what if the radius of the circle was, for instance 12, and not 1?

[@isaacsechslingloff8008]

Then everything gets scaled by 1 and you have 12 in the denominator of many parts of the proof. Eventually you can simplify it back to this but the chances of making a mistake are many.

[@isaacsechslingloff8008]

This works because of triangle similarity.

[@kingrobert7246]

@@isaacsechslingloff8008 thanks

[@gaurabkhatry7641]

How do i imagine if theta is quite big, like near 90degrees, how would the construction look like

[@ultrio325]

Just... don't.
Since theta is a variable we can draw in any size, so we draw the most convenient one.

[@seanpinto-escalante6359]

you lost me at 1:44 when you say that BC=ABcos(x)

[@divaythfyr575]

I am late. But cos(x) of triangle ABC returns the ratio adjacent/hypotenuse.
cos(x) = BC/AB
BC = ABcos(x)

[@dont_check_my_comment]

​@@divaythfyr575I am late for a Thank you

[@mindyourownbastardbu]

There's loads of words it's not very visual at all really

[@shiwaniranga1169]

Meri samajhh se bhar😓🤨