How do you simplify the expression 1/cos^2theta-1/cot^2theta?

1 Answer
Jim G.
Nov 19, 2016

1

Explanation:

Using the color(blue)"trigonometric identities"

color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(cottheta=costheta/sintheta" and " sin^2theta+cos^2theta=1)color(white)(2/2)|)))

rArr1/(cos^2theta)-1/(cot^2theta)=1/(cos^2theta)-1/(cos^2theta/sin^2theta

=1/(cos^2theta)-(sin^2theta)/(cos^2theta)

=(1-sin^2theta)/cos^2theta=cos^2theta/cos^2theta=1

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