Product to sum formulas for sin and cos - PROOF

[@mattl8930]

Thank you so much, it's so straight forward and understandable
You saved my life

[@ethanmullen4287]

Proving trig identities from other trig identities feels so wrong...but so right

[@MuPrimeMath]

The standard angle sum formulas can be proved geometrically, so we are free to use them!

[@ethanmullen4287]

@@MuPrimeMath that's why it feels right!

[@amrshamsel-deen7928]

Way to go
That Helped alot
in Fourier series

[@laze_amvs424]

Simple, Concise. Good job.

[@claireli88]

This is quite easily done. Thank you.

[@doggydoggywho]

This was so great. To the point and clear.

[@nitinsharma9840]

You just made it understandable ❤rather than memorising

[@Vengemann]

That's what I just needed thanks

[@captainzidgel7598]

Totally clear and concise. Thank you!

[@sportivescientist]

thankyou my lord
♥

[@krithy9331]

Smooth explanation 😄Thanks a ton..!

[@wintermelon8268]

Amazing video. Thank you!

[@josepineda8251]

Thanks for the help, pretty easy explanation

[@MuksEmmaN]

Thanks a ton big Bro needed this!

[@danielbesa-bs8iv]

Very helpful.....rather than memorising ❤

[@hasaanijaz145]

Well explained. Thank you.

[@patricksalhany8787]

Nice.
I like to go to the complex world and use Euler's formulas for cos and sin.

[@nuklearboysymbiote]

That can't be used to prove these identities. You needed trig identities to prove euler's. So that would be circular reasoning.

[@patricksalhany8787]

NukeML well I prove that e^(iθ)=cos(θ)+isin(θ) in a way other than using trig identities, then I use it to prove trig identities.

[@nuklearboysymbiote]

@@patricksalhany8787 the stage is all yours. go ahead.

[@patricksalhany8787]

One way to do it is to consider the function f such that f(θ)=(e^(iθ))/(cos(θ)+isin(θ)), then differentiate it with respect to θ and find that f'(θ)=0 for every θ, then f must be a constant, so you take a particular θ, say 0.
You can also prove it by using the definition of the complex cosine sine and expontial as series.

[@nuklearboysymbiote]

@@patricksalhany8787
Sorry I missed your reply. I've only just seen it. One nitpick is that the derivative of sine and cosine have to be proved using compound angle trig identities (related to the ones in this video), so you might be treading on circular reasoning.

[@Engineers-room]

Thx bro for this vid ♥️👌

[@farhanmax651]

great video ❤

[@fabiojr8082]

Thanks! How about a formula for tan(x)tan(y)?

[@ahmuuyi473]

very helpful

[@josephineakesser8437]

You're the best😘

[@Micana1980]

Tanx...... really helpful....

[@lorenzoklop5173]

Are you writing on the wall?

[@kentanakamura3263]

perfect thank you!

[@goldielocks9469]

Thank you 🙏

[@Uzumakifelt264]

Thanks a Lot man

[@Uzumakifelt264]

Why don't you put sum to product proof

[@sayote7639]

I just wanted to ask how can sin(a)cos(b )= sin(b)cos(a) and cos(a) doesn’t equal cos(b) nor does sin(a) equals sin(b)

[@wilmercuevas6491]

nice

[@ladusahu2000]

Clear

[@arefosman8255]

100th like :)

[@hiruki_neko]

Thank you!