Question

How do you prove `sin x/(1-cos x) + (1-cos x)/sin x = 2 csc x`?

Answer 1

one can prove it

Explanation:

`sin(x)/(1-cos(x))+(1-cos(x))/sin(x)=(sin(x)^2+(1-cos(x))^2)/(sin(x)(1-cos(x))`
The numerator is:
`sin(x)^2+1-2cos(x)+cos(x)^2=2(1-cos(x))`
So we get
`2/sin(x)`