Question

Simplify cos(x-y)+cos(x+y)/cosx

Answer 1

is the whole thing over cos(x) or is it just the cos(x+y) that is over cos(x)?

Answer 2

The whole thing is over cosx

Answer 3

okay do you know your sum and difference formulae for cos(x+y) and cos(x-y)?

Answer 4

Yes

Answer 5

so that's the first step. expand the top 2 terms like so:
\[\frac{\cos(x-y)+\cos(x-y)}{\cos(x)}=\]
\[\frac{(\cos(x)\cos(y)+\sin(x)\sin(y))+(\cos(x)\cos(y)-\sin(x)\sin(y))}{\cos(x)}=\]
the sin terms cancel out and the cos terms add together to give you:
\[\frac{2\cos(x)\cos(y)}{\cos(x)}=2\cos(y)\]
and that is your answer :)

Answer 6

oops the first part is actually:
\[\frac{\cos(x-y)+\cos(x+y)}{\cos(x)}\] sorry :)

Answer 7

Thanks very much

Answer 8

use tis identity 2cos x cos y = cos (x + y) + cos (x – y)
2cosxcosy/cosx=2cosy