Question

The value of sin² 20° + sin² 70° is __________.

Answer 1

We know that,
$\sin 70°=\sin \left(90°-20°\right)=\cos 20°\left[\sin \left(90°-\theta \right)=\cos \theta \right]$
$$\begin{gathered} \therefore {\sin }^{2}20°+{\sin }^{2}70° \\ ={\sin }^{2}20°+{\cos }^{2}20° \\ =1\left({\sin }^2\theta +{\cos }^2\theta =1\right) \end{gathered}$$

The value of sin² 20° + sin² 70° is _____1_____.