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.
Practice This ConceptMain explanation
Teacher explanation
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.
Example
If cot A = 2, then cosec squared A = 1 + 4 = 5, so cosec A = root 5 for an acute angle.
Simple analogy
Cotangent and cosecant travel together through the square identity.
Common confusion
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.
Answer writing and exam use
1-mark use
Write the exact meaning of identity 1 + cot^2 a = cosec^2 a in one clean line.
2-mark use
Define identity 1 + cot^2 a = cosec^2 a and add one example or condition.
3-mark use
Explain identity 1 + cot^2 a = cosec^2 a, show the method or example, and mention the common mistake.
Practice this concept with focused MCQs
Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.
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