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

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justaguide | College Teacher | (Level 2) Distinguished Educator

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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`