Question

prove that sin^2 theta + cos^2 theta = 1​

Answer 1

• sin theta=perpendicular/hypotenuse

• cose theta=base/hypotenuse

• sin^2theta+cos^2theta=(perpendicular/hypotenuse)^2+(base/hypotenuse)^2

=perpendicular^2/hypotenuse ^2+base^2/hypotenuse ^2

=perpendicular ^2+base^2/hypotenuse ^2

=hypotenuse ^2/hypotenuse ^2(by pythagorus theorem)

=1

hope it helped!

Answer 2

In any right angled triangle ABC, let ∠B is the right angle.

Using,  Pythagoras theorem

        AC² = BC² + AB²

sinA = height/hypotenuse = BC/AC

cosA = base/hypotenuse = AB/AC

         Square both sides and then add:

⇒ sin²A + cos²A = (BC/AC)² + (AB/AC)²

                      = BC²/AC² + AB²/AC²

                      = (BC² + AB²)/AC²

                      = AC²/AC²

                       = 1

Hence,  sin²A + cos²A = 1

In general we say  sin²θ + cos²θ = 1