Question 852861
Given;
(1) {{{sin^2(x) + sin^2(x)*cot^2(x)}}}
Use the identity
(2) {{{cot(x) = cos(x)/sin(x)}}}
and square both sides to get
(3) {{{cot^2(x) = cos^2(x)/sin^2(x)}}}
Now substitute (3) into (1) and get
(4){{{sin^2(x) + sin^2(x)*cos^2(x)/sin^2(x)}}} or
(5){{{sin^2(x) + cos^2(x)}}}
Since
(6) {{{sin^2(x) + cos^2(x) = 1}}}
You have
(7){{{sin^2(x) + sin^2(x)*cot^2(x) = 1}}}
Answer: 1
Also given
(8) {{{(sin^2(x) - 1)/cos(-x)}}}
Using (6) we get
(9) {{{sin^2(x) = 1 - cos^2(x) }}}
Now put (9) into (8) to get
(10) {{{( 1 - cos^2(x) - 1)/cos(-x)}}} or
(11){{{(-cos^2(x))/cos(-x)}}}  and 
Since the cosine is an even function we have
(12) {{{ cos(-x) = cos(x)}}}
Then (11) reduces to
(13) {{{-cos(x)}}}
Answer: {{{-cos(x)}}}