Identity sin^2 A + cos^2 A = 1
The identity sin squared A plus cos squared A equals 1 is a fundamental trigonometric relation for every angle A.
Practice This ConceptMain explanation
Teacher explanation
This identity comes from a right triangle. If the hypotenuse is taken as the common denominator, the squared opposite and adjacent parts add up to the square of the hypotenuse. After dividing by hypotenuse squared, the result becomes sin squared A plus cos squared A equals 1.
Example
If sin A = 3/5, then cos A = 4/5, and 9/25 + 16/25 = 25/25 = 1.
Simple analogy
Squares matter here: sine squared plus cosine squared gives one full unit.
Common confusion
Students sometimes write sin A plus cos A equals 1, but the squares are essential and cannot be removed.
Exam tip
Use this identity to check standard values or simplify expressions that contain both sin squared and cos squared terms.
Answer writing and exam use
1-mark use
Write the exact meaning of identity sin^2 a + cos^2 a = 1 in one clean line.
2-mark use
Define identity sin^2 a + cos^2 a = 1 and add one example or condition.
3-mark use
Explain identity sin^2 a + cos^2 a = 1, 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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