Question

if cos x+ cos y = a , sin x +sin y = b show cos(x-y) in terms of a and b..

Answer 1

cos(s-t) = cos s cos t + sin s sin t
Does that help?

Answer 2

i don't know what to do after that..

Answer 3

cos(x-y) = cos x (a - cos x) + sin x (b - sin x)

Answer 4

but the answer is \[(a ^{2}+b^{2}-2)\div2\]

Answer 5

so
= a cos x - cos^2 x + b sin x - sin^2 x
= a cos x + b sin x - 1
Sorry, someone else will have show me how I got off track with this one.

Answer 6

its okay.. thank you anyway..:)

Answer 7

Try working backword from the answer.

Answer 8

is cos x + cos y is the same as cos(x+y)?

Answer 9

No. But I got it now. Let me do it backward..

Answer 10

1/2(a^2 + b^2 - 2)
where
a^2 = cos^2 x + 2 cos x cos y + cos^2 y
b^2 = sin^2 x + 2 sin x siny + sin^2 y
so
a^2 + b^2 - 2 = 2 cos x cos y + 2 sin x siny
Multiply by 1/2 we have
cos x cos y + sin x sin y
which equals
cos (x-y)

Answer 11

ouhhh.. okie..

Answer 12

Yeah. I think it's right but I'd never have got there in the forward direction.

Answer 13

im trying to do in forward direction based from the backward direction you showed..

Answer 14

i think i get it..

Answer 15

Great!