Question

Prove that: sin² θ + cos² θ = 1

Answer 1

Let θ be an angle in a right-angled triangle with sides:

opposite = a, adjacent = b, hypotenuse = h

Using right‑triangle/Pythagorean approach:

sin θ = `a/h`

cos θ = `b/h`

`sin^2 θ + cos^2 θ = (a/h)^2 + (b/h)^2`

= `(a^2 + b^2)/h^2`

By the Pythagorean theorem,

a² + b² = h²

So, `(a^2 + b^2)/h^2 = h^2/h^2 = 1`

Therefore, sin² θ + cos² θ = 1