we are given with the function 1-sin^2 x / sinx - csc x and is asked in the problem to simplify the equation. we use trigonometric functions to determine the simplified form of the expression.
we all know by th etrigonometric identity of sums that cos^2x + sin^2x =1 and that csc x is the reciprocal of sin x or by expression: sinx = 1/csc x
Thus, we substitute to the expression on hand, 1-sin^2 x / sinx - csc x = cos^x / sinx - 1/sinx
cos^x / sinx - 1/sinx = cos^2x / sin^2x - 1/sinx = cos^2x * sin x /-cos^2x = -sinx. the final answer to this problem is equal to -sinx.