Question 1013469
i believe you are correct.


start with 1/cot^2(x) - 1/cos^2(x)


since cot^2(x) = cos^2(x)/sin^2(x), your expression becomes:


1/(cos^2(x)/sin^2(x)) - 1/cos^2(x)


since 1/(cos^2(x)/sin^2(x)) is equal to 1 * sin^2(x)/cos^2(x), your expression becomes:


sin^2(x)/cos^2(x) - 1/cos^2(x)


combine the terms under the common denominator to get:


(sin^2(x) - 1)/cos^2(x) = -(1 - sin^2(x))/cos^2(x) = -cos^2(x)/cos^2(x) = -1.


good work.