Question

Taking θ = 30° to verify the following trigonometric identity:

sin² θ + cos² θ = 1

Answer 1

Given: θ = 30°

To prove: sin² θ + cos² θ = 1

Proof:

L.H.S. = sin² θ + cos² θ

= sin² 30° + cos² 30°

= `(1/2)^2 + (sqrt 3/2)^2`

= `1/4 + 3/4`

= `4/4`

= 1

L.H.S. = R.H.S.

∴ sin² θ + cos² θ = 1