how would you prove csc(x)-sin(x)=cot(x)/sec(x) ?

Convert everything on the left to sine and cosine ratios first, then combine the fractions.

Monika (born in) 1993,

Did you try to convert everything on the left to sine and cosine ratios and did you then combine the fractions?

What was the result? Waiting to see what you found?
See

cosec(x)-sin(x)=cot(x)/sec(x)
1/sin x - sinx = cos x/sin x.sec x
(1 - sin ~2 x )/ sin x = cos~2 x / sin x
But, we know that 1 - sin ~2 x = cos ~2 x
Hence the result. Does it help?