Concept 8.3
sin²A + cos²A = 1 Is Pythagoras
Source: NCERT Mathematics, Class 108 minute lesson
Formal statement
For any acute angle A, sin²A + cos²A = 1. Dividing by cos²A or sin²A gives 1 + tan²A = sec²A and cot²A + 1 = cosec²A.
The intuition
Start from Pythagoras in the right triangle: opposite² + adjacent² = hypotenuse². Divide everything by hypotenuse².
The first fraction is sin²A, the second is cos²A, and the right side is 1. The identity is just Pythagoras, measured in units of the hypotenuse.
The attention
Look at where the identity comes from: Pythagoras.
sin²A + cos²A = 1 ⟸ opp² + adj² = hyp² divided by hyp²
Look hereNot here
- Look here
- Pythagoras, where it comes from. Every one of these identities is the same theorem divided by one of the sides squared.
- Not here
- The squared ratio, (sin A)². sin²A means (sin A)², not sin(A²). Treating it as the square of the angle breaks every calculation.
- What it teaches
- If you can derive a formula in one line, you never have to memorise it.