Question

integrate sin(2x)/sin(x). The Answer is 2sin(x)+c why and how?

Answer 1

The farthest I have gotten is to turn it into sin(2x)*sec

Answer 2

sin(2x)/sin(x)

sin(2x) = sinx (x + x) = sinx cos x + sin x cos x = 2 sinx cosx

2 sinx cosx / sin x
2 cos x

Integral of cos x = sin x

2 * sin x

Answer 3

The answer is 2sin(x)

Answer 4

How'd you turn sin(2x) into sinx*cosx+sinx*cosx

Answer 5

Is it just an identity?

Answer 6

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

Answer 7

Is it possible to do this by parts?

Answer 8

I don't know, perhaps, but I don't see why you'd want that. It's so much simpler to just cancel sinx...

Answer 9

Fair enough.