I just derived a sketchy series representing cos²x this morning, however, I don't know if it's correct. Heck, I can't even extrapolate a general term U_n

So, if you've done it before, or seen it, kindly drop the U_n term. As I need it to prove something.

Mine went like this . .


1 - x² + x⁴/3 - 2x⁶/45 + . . . .

Is it correct?

So that the thread won't die!




But who all these equations don help?

WTF!

I be olodo but that doesn't stop me from donating a comment

















Op, correct is the equation. I asked ifa

1- x^2+ x^4/3+.... (Taylor series) That's the Maclaurin Expansion. The Maclaurin expansion is a special case of the Taylor Series for x=0. How did you do your "proof"?

@hahn and @karmanaut

Thanks a lot. I was looking to clarify that before I began the proof . . . now I can proceed,

However, my glasses are now destroyed . . . and I literally can't see anything beyond 30 centimeters. (In fact, as I type this, my phone is like, three inches from my face. )

So, when I get them fixed, my vision will return, and I'll post what I'm trying to proof, as well as the proof.

@Robinhez . . . what if I told you to find sin x without use of calculator or tables?n
Then will these equations help you.

known that

cos²x = 0.5(1+ cos2x)

thus => 0.5[1 + ( 1 -4x^2 /2! + 16x^4 /4! - . . . )]

=> 0.5[ 1 + £ (-1)ⁿ (2x)²ⁿ /(2n)! ]

(£ = sigma, summation )
for n= 0,1,2,3. . . .


guess that's it.