For any angle θ, state the value of :

sin² θ + cos² θ.

1

Reason:

sin² θ + cos² θ = 1

Let take θ = 30°

sin² 30° = $\Big(\dfrac{1}{2}\Big)^2 = \dfrac{1}{4}$

cos² 30° = $\Big(\dfrac{\sqrt3}{2}\Big)^2 = \dfrac{3}{4}$

Now, sin² 30° + cos² 30°

$= \dfrac{1}{4} + \dfrac{3}{4}\\[1em] = \dfrac{1 + 3}{4}\\[1em] = \dfrac{4}{4}\\[1em] = 1$