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.
In one line: Squares matter here: sine squared plus cosine squared gives one full unit.
Practice This ConceptUnderstand it
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
Formula and rule
sin2 A + cos2 A = 1 for every angle A.
This is a basic identity and is often used as a starting point for other identities.
See it worked out
Follow the example line by line, then use the same method on new questions.
Worked example
If sin A = 5/13, then cos A = 12/13 by the identity, because 25/169 + 144/169 = 169/169 = 1.
Method you can reuse
- 1Square the known ratio.
- 2Subtract from 1 if the missing ratio is required.
- 3Take the square root.
- 4Choose the positive value for an acute angle.
Check yourself
Answer the question in your head before opening the answer.
Try it yourself
If sin A = 4/5, what should cos A be for this identity to hold?
Think first, then show answerHide answer
Common wrong answer
A common wrong answer is to forget the squares and use sin A plus cos A equals 1. That is not the correct identity.
Don't mix this up
Exam tip
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
- 1
Enough for 1 mark
The identity sin squared A plus cos squared A equals 1 is a fundamental trigonometric relation for every angle A.
- 2
Add for 2 marks
Example: If sin A = 3/5, then cos A = 4/5, and 9/25 + 16/25 = 25/25 = 1.
- 3
Add for 3 marks
This identity comes from a right triangle.
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