Maclaurin series of sin^2x 

Prime Newtons is my prime source of math knowledge. Bravo, sir! 🎉😊

We can also try to express sin^2(x) in terms of e^(i.2x) and e^(-i.2x). The Maclaurin series of the function e^(ix) is also well known.

I rarely comment on videos, but I have to say: The way you present these concepts is amazing!

I find the analysis and explanations in this series just wonderful. While a PhD or advanced degree is certainly not a requirement to be smart and be able to get information across, it is very rare I think to find someone who apparently does not have those qualifications do such an incredible job. Where did you the scope of your knowledge of mathematics that you so clearly Express? Keep it up and don’t stop.

This was fun .... And literally a beautiful result. An equation that gives you what you need is nothing short of that word. Loved your explanation once again, Prime Newtons!

As a maths educator and youtube creator, one of my fav channels to follow is Prime Newtons.

So neat, the way you explain it. I wish all math students have a chance to view your channel! .

Can't we use that sin^2(x)=(1-cos(2x)/2 and the Maclaurin series for cos(x)?

You are the most gifted teacher! I was trying to find your older video of solving (x+7)^7= x^7 + 7^7 , to show it to the friend, it took me a while. If you put the equations on the title it is easy to find them easily in RU-vid too.

How do you recommend a problem? I have one function I'd like you to look at that I've written that I think would be interesting to explore. Thank you for all of the maths that you do, and learning you facilitate!

Bro added life lesson for climatic end 😂

Very cool! 😎

Another way of doing this is to take the Maclaurin series for sin(x) and square that series.

My dumbass would do (x-x³/3!+x⁵/5!)²😂

Thank you

Maclaurin series of f(x)=2 x=(1-cos(2x))/2 sin

sin^2(x)=(1-cos(2x))/2 cos(x)=sum[n=0,♾️]((-1)^n•x^(2n)/(2n)!) cos(2x)=sum[n=0,♾️]((-4)^n•x^(2n)/(2n)!) sin^2(x)=sum[n=1,♾️]((-1)^(n+1)•2^(2n-1)•x^(2n)/(2n)!)