Question

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

sin²θ + cos²θ = 1

Answer 1

Given: θ = 30°

To prove: sin²θ + cos²θ = 1

Proof:

L.H.S. = sin²θ + cos²θ

= sin²30° + cos²30°

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

= `1/4 + 3/4`

= `4/4`

= 1

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

∴ sin²θ + cos²θ = 1