Trig Identites, Need Help ASAP?

Question

Can you please show me the steps in solving this problem. Work one side of the equation.

1 + cosx................sinx
________ = _________

sinx....................1 - cosx


(pretend the dots are not there, I did that to allign the numbers under the division sign)
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Answer 1

Prove the identity (1 + cosx)/sinx = sinx/(1 - cosx)

Let's work with the Right Hand Side.

Right Hand Side = sinx/(1 - cosx)
= sinx(1 + cosx) / [(1 - cosx)(1 + cosx)]
= sinx(1 + cosx) / (1 - cos²x)
= sinx(1 + cosx) / sin²x
= (1 + cosx) / sinx = Left Hand Side

Answer 2

recall the identity (sin(x))^2 + (cos(x))^2 =1. that is what you are looking here.
as with any rational problem it can be solve by multiplying each side by the denominators. the result will be
(1-cosx)(1+cosx)=(sinx)^2
when you finsih multiplying the left side and solving the equation 1=the identity

Answer 3

(1 + cosx)/sinx = (1 + cosx)(1 - cosx)/sinx(1 -cosx) ie multiply top and bottom by (1 -cosx)

The denominator is (1 +cosx)(1 -cosx) = (1 - cos^2x) = sin^2x

Thus (1 + cosx)/sinx = (1 + cosx)(1 - cosx)/sinx(1 -cosx) = sin^2x/sinx(1 - cosx) = sinx/(1 -cosx) which is the RHS qed

Answer 4

Alright. Take the first equation and multiply the top and bottom by 1 - cos(x).

On the top you get 1 - cos(x)^2
And on the bottom you get sin(x) - sin(x)*cos(x)

You use a trig identity to get 1 - cos(x)^2=sin(x)^2
Then, cancel the sin(x)'s on the top and bottom.

You get sin(x)/(1 - cos(x))