Question

Use the angle addition formula to find the expression for cos (a+b). What happens if you change it to cos(a+a)

Answer 1

look at page 2 of this trig identity sheet

http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf

Answer 2

look at page 2 of the `Sum and Difference Formulas` section

you'll see this identity

\[\Large \cos\left(\alpha \pm \beta\right) = \cos\left(\alpha\right)\cos\left(\beta\right)\mp\sin\left(\alpha\right)\sin\left(\beta\right)\]

Answer 3

In your case, it means

\[\Large \cos\left(a +b\right) = \cos\left(a\right)\cos\left(b\right)-\sin\left(a\right)\sin\left(b\right)\]

Answer 4

You pretty much have to remember that "sum formula for the cosine" as well as the "sum formula for the sine."

To answer the 2nd part of your question: Take Jim's latest input and replace that "b" with "a." What does cos (a + a) come out to? Note that we can write cos (a+a+ as cos 2a.

Answer 5

\[\cos(a+a) = \cos(2a) = \cos^2(a) - \sin^2(a) = 2\cos^2(a)-1 = 1 - 2\sin^2(a)\]

Answer 6

Yes...there's more than one correct formula for cos 2a = cos (a+a). Thx, Sir Box.