Question

prove that sin(x) x 1+cos(x) / 1+cos(x) x sin(x) = 2csc(x)

Answer 1

I don't think you wrote what you meant to write... Please rewrite with CAREFUL use of parenthesis.

This is exactly what you wrote, and it's false
\[1 \cdot x\cdot sin(x)+\frac{cos(x)}{1}+x \cdot cos(x) \cdot sin(x) = 2 \cdot csc(x)\]

Answer 2

It's alright lots of people here on this site forget parenthesis, but they are important here so people know what you intended to write. ;-)

Answer 3

Sorry about that, here is a picture of the problem.

Answer 4

Typing it up...
\[\frac{(\sin\theta \cos\theta)}{(1+\cos\theta \sin\theta)} = 2 \csc\theta=\frac{2}{sin \theta}\]

Ok, now what are you doing with this identity? If you're trying to prove it, try multiplying it by something that gets rid of the denominators.

Answer 5

\[ (sin\theta)(1+cos\theta sin\theta) \] to both sides, agreed?

Answer 6

Basically, cross multiply and simplify

Answer 7

Okay, thank you so much. :)