Simplify the expression sin(x+y) - sin(x-y)?

Question

the answer choices are:

a) sin(2xy)

b) 2cos(x)sin(y)

c) 2sin(x)cos(y)

d) cos(x)sin(y)

Answer 1

This is funnnnnnn.

Recall:

sin (A + B) = sin A cos B + cos A sin B

sin (A - B) = sin A cos B - cos A sin B

So:

sin (x + y) - sin (x - y)

= sin x cos y + cos x sin y - [sin x cos y - cos x sin y]

= sin x cos y + cos x sin y - sin x cos y + cos x sin y

= 2 cos x sin y.

= option b).

I hope that helps. :)

me07.