Question

Find the value of sin²33° + sin²57°.

Answer 1

We have
$\sin 57°=\sin \left(90°-33°\right)=\cos 33°\left[\sin \left(90°-\theta \right)=\cos \theta \right]$
$$\begin{gathered} \therefore {\sin }^{2}33°+{\sin }^{2}57° \\ ={\sin }^{2}33°+{\cos }^{2}33° \\ =1\left({\sin }^2\theta +{\cos }^2\theta =1\right) \end{gathered}$$

Thus, the value of sin²33° + sin²57° is 1.