Question 1153470
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Simplify the first term on the left by expressing everything in sin(x) and cos(x), and using sin(-x) = -sin(x):<br>
{{{-1/csc(-x) = -sin(-x) = -(-sin(x)) = sin(x)}}}<br>
Similarly, simplify the second term on the left:<br>
{{{cot(-x)/sec(-x) = (cos(-x)/sin(-x))/(1/cos(-x)) = (cos^2(-x)/sin(-x)) = (-cos^2(x)/sin(x))}}}<br>
The expression on the left is now<br>
{{{sin(x)-(-cos^2(x)/sin(x)) = sin(x)+(cos^2(x)/sin(x))}}}<br>
Combine terms using a common denominator and use sin^2(x)+cos^2(x)=1:<br>
{{{(sin^2(x)+cos^2(x))/sin(x) = 1/sin(x) = csc(x)}}}<br>