Trig identities......?

Question

I need to know the process for:


(Csc(x) - sin(x)) / cot^2 (x) = sin (x)

I've tried and have gotten it to equal 1/cot(x), but can't get any further then there.

Added:

Please remember the left side of the equation is divided by COTANGENT not cosine.

Answer 1

(1/sin - sin) / cos^2/sin^2
(sin - sin^3)/ cos^2 = sin (1 - sin^2)/cos^2

since cos^2 + sin^2 = 1 then cos^2 = 1 - sin^2

= sin cos^2/cos^2 = sin

Answer 2

ok, i am ignoring the parameter x for convenience.

(cosec - sin)/ (cot ^2)



substitute cosec as 1/sin

cot^2 as cos^2/sin^2

equation reads:

=(1/sin-sin )/ (cos^2/sin^2)

=(1-sin^2)/(cos^2/sin)

since, cos^2+sin^2=1

=cos^2 * (sin/cos^2)

=sin

YAY!

Answer 3

1/sin(x) - sin(x) / (cos(x)^2 / sin(x)^2)

sin(x) - sin(x)^3 / cos(x)^2 (since cosx^2 -1 = sin(x)^2)

sin(x) - sin(x)^3 / (1 - sin(x)^2)

sin (1- sin^2) / (1 - sin^2)

sin(x)