To prove:
sin²θ + cos²θ = 1

Proof:
In a right-angled triangle,
sinθ = opposite / hypotenuse
cosθ = adjacent / hypotenuse

Now,
sin²θ + cos²θ = (opposite² + adjacent²) / hypotenuse²

By Pythagoras theorem,
opposite² + adjacent² = hypotenuse²

So,
sin²θ + cos²θ = hypotenuse² / hypotenuse² = 1

Hence proved.