Identity 1 + tan^2 A = sec^2 A
The identity 1 plus tan squared A equals sec squared A is a standard trigonometric identity used for simplification and verification.
Practice This ConceptMain explanation
Teacher explanation
This identity is derived from the basic relation sin squared A plus cos squared A equals 1. If the whole equation is divided by cos squared A, the result becomes 1 plus tan squared A equals sec squared A. It is very useful when a problem contains tangent and secant together.
Example
If tan A = 2, then sec squared A = 1 + 4 = 5, so sec A = root 5 for an acute angle.
Simple analogy
Tangent to secant is a square-step identity: square first, then add one.
Common confusion
Students often write 1 plus tan A equals sec A, but the squares are required on both trig terms.
Exam tip
Whenever tangent is given and secant is needed, use this identity directly instead of building a triangle again.
Answer writing and exam use
1-mark use
Write the exact meaning of identity 1 + tan^2 a = sec^2 a in one clean line.
2-mark use
Define identity 1 + tan^2 a = sec^2 a and add one example or condition.
3-mark use
Explain identity 1 + tan^2 a = sec^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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