Identity 1 + cot^2 A = cosec^2 A

1. Square cot A. 2. Add 1. 3. If needed, take the square root for cosec A. 4. Keep the angle acute if a positive value is required.

A right triangle with angle A helps students remember that cot and cosec are linked through the same angle and the same sides.

A common wrong answer is to treat cot and cosec as if they are direct neighbors and forget the square relation.

The identity 1 plus cot squared A equals cosec squared A is a standard trigonometric relation used for simplification and checking answers.

The identity 1 plus cot squared A equals cosec squared A is a standard trigonometric relation used for simplification and checking answers. 1 + cot^2 A = cosec^2 A. This comes from dividing sin^2 A + cos^2 A = 1 by sin^2 A. If cot A = 2, then cosec squared A = 1 + 4 = 5, so cosec A = root 5 for an acute angle.

This identity is obtained from the basic identity by dividing throughout by sin squared A. It links cotangent and cosecant, so it is very useful when a question gives cot A and asks for cosec A, or when an expression needs simplification. 1 + cot^2 A = cosec^2 A. This comes from dividing sin^2 A + cos^2 A = 1 by sin^2 A. If cot A = 1/3, then cosec squared A = 1 + 1/9 = 10/9, so cosec A = root 10 over 3 for an acute angle. CBSE may ask for the missing cosec value, or ask you to verify an identity in algebraic form. A common wrong answer is to treat cot and cosec as if they are direct neighbors and forget the square relation.