(1)

\[

\begin{aligned}

& \cos 6 A=\cos [2(3 A)] \\

& \therefore \cos 6 A=\cos ^2 3 A-\sin ^2 3 A \\

& \therefore \cos 6 A=2 \cos ^2 3 A-1 \\

& \therefore \cos 6 A=1-2 \sin ^2 3 A

\end{aligned}

\]

(2)

\[

\begin{aligned}

& \cos 80^{\circ}=\cos \left[2\left(40^{\circ}\right)\right] \\

& \therefore \cos 80^{\circ}=\cos ^2 40^{\circ}-\sin ^2 40^{\circ} \\

& \therefore \cos 80^{\circ}=2 \cos ^2 40^{\circ}-1 \\

& \therefore \cos 80^{\circ}=1-2 \sin ^2 40^{\circ}

\end{aligned}

\]

(3)

\[

\begin{aligned}

& \cos A=\cos \left[2\left(\frac{A}{2}\right)\right] \\

& \therefore \cos A=\cos ^2 \frac{A}{2}-\sin ^2 \frac{A}{2} \\

& \therefore \cos A=2 \cos ^2 \frac{A}{2}-1 \\

& \therefore \cos A=1-2 \sin ^2 \frac{A}{2}

\end{aligned}

\]