As, cosecx, secx and cotx are just the reciprocals of sinx, cosx and tanx, when you multiply each corresponding pair you just get 1. This results in 1*1*1 giving a final answer of 1.
The problem asked for the product by multiplying all the six trigonometric functions. We need to understand that csc(x) is just the reciprocal or the inverse of sin(x). That would mean if we multiply then together it would result to 1. This is also true with sec(x) and cos(x) and also cot(x) and tan(x). So that is multiplying three 1's which results to one.
