(a)

\[

\begin{aligned}

& 2 \sin 15^{\circ} \cdot \cos 15^{\circ} \\

& =\sin \left[2\left(15^{\circ}\right)\right] \\

& =\sin 30^{\circ} \\

& =\frac{1}{2}

\end{aligned}

\]

(b)

\[

\begin{aligned}

& 1-2 \cos ^2 22,5^{\circ} \\

& =-\left(2 \cos ^2 22,5^{\circ}-1\right) \\

& =-\left[\cos \left(2\left(22,5^{\circ}\right)\right]\right. \\

& =-\cos 45^{\circ} \\

& =-\frac{\sqrt{2}}{2}

\end{aligned}

\]

(c) \(\begin{aligned} & \left(\cos 15^{\circ}+\sin 15^{\circ}\right)^2 \\ = & \cos ^2 15^{\circ}+2 \cos 15^{\circ} \cdot \sin 15^{\circ}+\sin ^2 15^{\circ} \\ = & \cos ^2 15^{\circ}+\sin ^2 15^{\circ}+2 \sin 15^{\circ} \cdot \cos 15^{\circ} \\ = & 1+\sin \left[2\left(15^{\circ}\right)\right] \\ = & 1+\sin 30^{\circ} \\ = & 1+\frac{1}{2}=\frac{3}{2}\end{aligned}\)