Question

cos(x+y) + cos(x+y) = 2cos(x+y)

What is this process called again? Simplification? Sorry, having a slow moment.

Answer 1

Simplification would be a good term for that.

Answer 2

http://ocw.mit.edu/resources/res-18-005-highlights-of-calculus-spring-2010/derivatives/derivative-of-sin-x-and-cos-x/
The two key functions of oscillation have specially neat derivatives: The slope of sin x is cos x ! And the slope of cos x is - sin x.

These come from one crucial fact: (sin x) / x approaches 1 at x = 0. This checks that the slope of sin x is cos 0 = 1 at the all-important point x = 0.

Professor Strang connects sine and cosine to moving around a circle,
or up and down for a spring, or in and out for your lungs.

Professor Strang's Calculus textbook (1st edition, 1991) is freely available here.

Subtitles are provided through the generous assistance of Jimmy Ren.

Answer 3

How about a more obvious explanation:

x + x = 2x
2x = 2x

x^2 + x^2 = 2x^2
2x^2 = 2x^2


(a+b) + (a+b) = 2(a+b)
2(a+b) = 2(a+b)


cos(x+y) + cos(x+y) = 2cos(x+y)
2cos(x+y) = 2cos(x+y)

Answer 4

It's called adding like terms by the way