Question

Prove that sin^2(a) + cos^(a) = 1

Answer 1

To Prove

sin²(a) + cos²(a) = 1

$\rule{50}2$

Proof

We know that, in a right angled triangle, for an angle "a", sin(a) = Perpendicular/Hypotenuse, or sin(a) = P/H.

We also know that cos(a) = Base/Hypotenuse, or cos(a) = B/H

Hence, sin²(a) + cos²(a) can be written as

(P/H)² + (B/H)²

→ P²/H² + B²/H²

→ $\sf\frac{P^2 + B^2}{H^2}$

→ $\sf\frac{H^2}{H^2}$

(Since, by Pythagoras theorem, in a right angled triangle P² + B² = H²)

→ $\sf 1$

Or, cos²(a) + sin²(a) = 1

Hence Proved.