Question

Can someone help me with two questions? Will medal!

Answer 1

Verify the Identity:
cos (x-y) - cos (x+y) = 2 sin x sin y

Please show steps!

Answer 2

please apply these identities:
\[\cos(x-y)=\cos x \cos y +\sin x \sin y\]
and:
\[\cos(x+y)=\cos x \cos y -\sin x \sin y\]

Answer 3

I do not understand how to do that please explain?

Answer 4

please substitute \[\cos x \cos y +\sin x \sin y \]
in place of cos(x-y)
and
\[\cos x \cos y -\sin x \sin y\]
in place of cos(x+y)

Answer 5

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

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

??

Answer 6

ok!

Answer 7

Is that correct?

Answer 8

yes! since the left side is equal to the right side

Answer 9

Thank you! I'll start a new question for the next one I need help with and medal awarded :)

Answer 10

ok! Thank you!