Question

prove that cos2 A + sin2 A = 1​

Answer 1

Kindly refer the attachment! :D

TO PROVE:

sin²A + cos²A = 1

PROOF:

Consider right △ ABC, where ∠B = 90⁰

a,b and c are side of the triangle ABC,

Sin A = Opposite side/ Hypotenuse

∴ Sin A = a/b ------- (1)

Cos θ = Adjacent side/Hypotenuse

∴ Cos A = c/b ------- (2)

By Pythagoras theorem, in △ ABC

Base² + Altitude² = Hypotenuse²

==> a² + c² = b²

• Now, divide the whole equation by b²

==> a²/b² + c²/b² = b²/b²

==> (a/b)² + (c/b)² = 1

• Substituting equations (1) and (2),

==> Sin²A + Cos²A = 1

Hence, proved ✅