Simplify `1/(cos^2 x) - 1/(cot^2 x)`

Expert Answers
justaguide eNotes educator| Certified Educator

The expression `1/(cos^2 x) - 1/(cot^2 x)` has to be simplified

`1/(cos^2 x) - 1/(cot^2 x)`

=> `1/(cos^2x) - (sin^2x)/(cos^2x)`

=> `(1 - sin^2x)/(cos^2x)`

=> `(cos^2x)/(cos^2x)`

=> 1

The expression `1/(cos^2 x) - 1/(cot^2 x) = 1`

jeew-m eNotes educator| Certified Educator

`1/(cos^2x)-1/(cot^2x)`

`= sec^2x-tan^2x`

`= 1+tan^2x-tan^2x`

`= 1`