Given the right triangle DeltaABC as shown fill in the value

Given the right triangle DeltaABC as shown, fill in the values of sin theta and cos theta, and prove that sin^2 theta + cos^2 theta =1.

Solution

From the right triangle, using pythagorean theorem a² + b² = c²

sin = (opposite side)/(hypotenuse) = a/c

cos = (adjacent side)/(hypotenuse) = b/c

sin² + cos² = 1

consider sin² + cos²

= (a/c)² + (b/c)²

= a²/c² + b²/c²

= (a² + b²)/c²

= c²/c²

= 1

Hence sin² + cos² = 1