Question

Is there a quicker way to find "(cos(x+y))^2 + (sin(x-y))^2" ? (The answer is 1-sin2x*sin2y)

Answer 1

I think your best bet would be to look up the formulas for cos (x+y) and sin (x-y) (which are called "sum formula for the cosine" and "difference formula for the sine". Looks as though you'll have square both...unless you can find an identity for 1-sin2x*sin2y).

By the way, do you mean (sin x)^2 or do you mean sin (2x)? Can't tell.

Answer 2

Thanks. I found the answer by applying the summation formulas and it took so much time yet it was a multiple choice question and I wondered maybe there was a shortcut.
I mean (sin x)^2

Answer 3

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

Answer 4

Then I think you can see what to do from there? :P

Answer 5

Thanks