SOLUTION: Simplify the following expression. 1/(cot^2(x)) - 1/(cos^2(x)) I think I've figured it out to be -1? but I'd just like to be sure. Thank you!

Algebra ->  Trigonometry-basics -> SOLUTION: Simplify the following expression. 1/(cot^2(x)) - 1/(cos^2(x)) I think I've figured it out to be -1? but I'd just like to be sure. Thank you!      Log On


   

Question 1013469: Simplify the following expression.
1/(cot^2(x)) - 1/(cos^2(x))
I think I've figured it out to be -1? but I'd just like to be sure. Thank you!
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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.