medium difficulty5 min

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

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

In one line: Cotangent and cosecant travel together through the square identity.

Practice This Concept

Understand it

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.

Formula and rule

1 + cot² A = cosec² A.

This comes from dividing sin² A + cos² A = 1 by sin² A.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

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.

Method you can reuse

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

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

If cot A = 5, what is cosec squared A?

Think first, then show answer

cosec squared A = 1 + cot squared A = 1 + 25 = 26. The square is required before adding 1.

Common wrong answer

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

Don't mix this up

Students sometimes write 1 plus cot A equals cosec A, but the squared form is the correct one.

Exam tip

Use this identity when cotangent is given and cosecant is required; it saves time in step-by-step algebra.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

CBSE may ask for the missing cosec value, or ask you to verify an identity in algebraic form.

1
Enough for 1 mark
The identity 1 plus cot squared A equals cosec squared A is a standard trigonometric relation used for simplification and checking answers.
2
Add for 2 marks
Example: If cot A = 2, then cosec squared A = 1 + 4 = 5, so cosec A = root 5 for an acute angle.
3
Add for 3 marks
This identity is obtained from the basic identity by dividing throughout by sin squared A.

MCQ Quiz

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