Vraag 12

Goniometrie

\sin\left(t+u\right)=\sin\left(t\right)\cos\left(u\right)+\cos\left(t\right)\sin\left(u\right)\sin\left(tu\right)=\sin\left(t\right)\cos\left(u\right)+\cos\left(t\right)\sin\left(u\right)\sin\left(t-u\right)=\sin\left(t\right)\cos\left(u\right)+\cos\left(t\right)\sin\left(u\right)\sin\left(t-u\right)\sin\left(t\right)\cos\left(u\right)+\cos\left(t\right)\sin\left(u\right)\sin\left(t-u\right)-\sin\left(t\right)\cos\left(u\right)+\cos\left(t\right)\sin\left(u\right)\sin\left(t-u\right)-\sin\left(t\right)\cos\left(u\right)\cos\left(t\right)\sin\left(u\right)\sin\left(t-u\right)-\sin\left(t\right)\cos\left(u\right)-\cos\left(t\right)\sin\left(u\right)\sin\left(t+u\right)=\sin\left(t+u\right)\sin\left(t+u\right)\sin\left(t+\right)\sin\left(t+i\right)\sin\left(t+\right)\sin\left(t\right)\sin\left(\right)\sinsis

\sin\left(t-u\right)=\sin\left(t\right)\cos\left(u\right)-\cos\left(t\right)\sin\left(u\right)\sin\left(t-u\right)\sin\left(t\right)\cos\left(u\right)-\cos\left(t\right)\sin\left(u\right)\sin\left(t-u\right)-\sin\left(t\right)\cos\left(u\right)-\cos\left(t\right)\sin\left(u\right)\sin\left(t-u\right)-\sin\left(t\right)\cos\left(u\right)-\cos\left(t\right)\sin\left(u\right)\sin\left(t-u\right)-\sin\left(t\right)\cos\left(u\right)-\cos\left(t\right)\sin\left(\right)\sin\left(t-u\right)-\sin\left(t\right)\cos\left(u\right)-\cos\left(t\right)\sin\sin\left(t-u\right)-\sin\left(t\right)\cos\left(u\right)-\cos\left(t\right)si\sin\left(t-u\right)-\sin\left(t\right)\cos\left(u\right)-\cos\left(t\right)s\sin\left(t-u\right)-\sin\left(t\right)\cos\left(u\right)-\cos\left(t\right)\sin\left(t-u\right)-\sin\left(t\right)\cos\left(u\right)-\cos\left(t\right)\sin\left(t-u\right)-\sin\left(t\right)\cos\left(u\right)-\cos\left(\right)\sin\left(t-u\right)-\sin\left(t\right)\cos\left(u\right)-\cos\sin\left(t-u\right)-\sin\left(t\right)\cos\left(u\right)-co\sin\left(t-u\right)-\sin\left(t\right)\cos\left(u\right)-c\sin\left(t-u\right)-\sin\left(t\right)\cos\left(u\right)-\sin\left(t-u\right)-\sin\left(t\right)\cos\left(u\right)\sin\left(t-u\right)-\sin\left(t\right)\cos\left(u\right)\sin\left(t-u\right)-\sin\left(t\right)\cos\left(\right)\sin\left(t-u\right)-\sin\left(t\right)\cos\sin\left(t-u\right)-\sin\left(t\right)co\sin\left(t-u\right)-\sin\left(t\right)c\sin\left(t-u\right)-\sin\left(t\right)\sin\left(t-u\right)-\sin\left(t\right)\sin\sin\left(t-u\right)-\sin\left(t\right)\sin\left(\right)\sin\left(t-u\right)-\sin\left(t\right)\sin\sin\left(t-u\right)-\sin\left(t\right)si\sin\left(t-u\right)-\sin\left(t\right)s\sin\left(t-u\right)-\sin\left(t\right)\sin\left(t-u\right)-\sin\left(t\right)c\sin\left(t-u\right)-\sin\left(t\right)c\in\sin\left(t-u\right)-\sin\left(t\right)c\in s\sin\left(t-u\right)-\sin\left(t\right)c\in\sin\left(t-u\right)-\sin\left(t\right)ci\sin\left(t-u\right)-\sin\left(t\right)c\sin\left(t-u\right)-\sin\left(t\right)\sin\left(t-u\right)-\sin\left(t\right)\sin\left(t-u\right)-\sin\left(\right)\sin\left(t-u\right)-\sin\sin\left(t-u\right)-si\sin\left(t-u\right)-s\sin\left(t-u\right)-\sin\left(t-u\right)\sin\left(t-u\right)\sin\left(t-\right)\sin\left(t\right)\sin\left(\right)\sinsis

\cos\left(t+u\right)=\cos\left(t\right)\cos\left(u\right)-\sin\left(t\right)\sin\left(u\right)\cos\left(t+u\right)=\cos\left(t\right)\cos\left(u\right)\sin\left(t\right)\sin\left(u\right)\cos\left(t+u\right)=\cos\left(t\right)\cos\left(u\right)+\sin\left(t\right)\sin\left(u\right)\cos\left(tu\right)=\cos\left(t\right)\cos\left(u\right)+\sin\left(t\right)\sin\left(u\right)\cos\left(t-u\right)=\cos\left(t\right)\cos\left(u\right)+\sin\left(t\right)\sin\left(u\right)

\cos\left(t-u\right)=\cos\left(t\right)\cos\left(u\right)+\sin\left(t\right)\sin\left(u\right)\cos\left(t-u\right)=\cos\left(t\right)\cos\left(u\right)+\sin\left(t\right)\sin\left(u\right)\cos\left(t-u\right)=\cos\left(t\right)\cos\left(u\right)+\sin\left(t\right)\sin\left(\right)\cos\left(t-u\right)=\cos\left(t\right)\cos\left(u\right)+\sin\left(t\right)\sin\cos\left(t-u\right)=\cos\left(t\right)\cos\left(u\right)+\sin\left(t\right)si\cos\left(t-u\right)=\cos\left(t\right)\cos\left(u\right)+\sin\left(t\right)s\cos\left(t-u\right)=\cos\left(t\right)\cos\left(u\right)+\sin\left(t\right)\cos\left(t-u\right)=\cos\left(t\right)\cos\left(u\right)+\sin\left(t\right)\cos\left(t-u\right)=\cos\left(t\right)\cos\left(u\right)+\sin\left(t\right)\cos\left(t-u\right)=\cos\left(t\right)\cos\left(u\right)+\sin\left(\right)\cos\left(t-u\right)=\cos\left(t\right)\cos\left(u\right)+\sin\cos\left(t-u\right)=\cos\left(t\right)\cos\left(u\right)+si\cos\left(t-u\right)=\cos\left(t\right)\cos\left(u\right)+s\cos\left(t-u\right)=\cos\left(t\right)\cos\left(u\right)+\cos\left(t-u\right)=\cos\left(t\right)\cos\left(u\right)\cos\left(t-u\right)=\cos\left(t\right)\cos\left(u\right)-\cos\left(t-u\right)=\cos\left(t\right)\cos\left(u\right)\cos\left(t-u\right)=\cos\left(t\right)\cos\left(u\right)=\cos\left(t-u\right)=\cos\left(t\right)\cos\left(u\right)\cos\left(t-u\right)=\cos\left(t\right)\cos\left(u\right)\cos\left(t-u\right)=\cos\left(t\right)\cos\left(\right)\cos\left(t-u\right)=\cos\left(t\right)\cos\cos\left(t-u\right)=\cos\left(t\right)co\cos\left(t-u\right)=\cos\left(t\right)c\cos\left(t-u\right)=\cos\left(t\right)\cos\left(t-u\right)=\cos\left(t\right)\cos\left(t-u\right)=\cos\left(\right)\cos\left(t-u\right)=\cos\cos\left(t-u\right)=co\cos\left(t-u\right)=c\cos\left(t-u\right)=\cos\left(t-u\right)\cos\left(t-u\right)-\cos\left(t-u\right)\cos\left(t-\right)\cos\left(t-\right)\cos\left(t\right)\cos\left(t0\right)\cos\left(t\right)\cos\left(\right)\coscoc

\sin\left(2t\right)=2\sin\left(t\right)\cos\left(t\right)\sin\left(2t\right)=2\sin\left(t\right)\cos\left(t\right)\sin\left(2t\right)=2\sin\left(t\right)\cos\left(\right)\sin\left(2t\right)=2\sin\left(t\right)\cos\sin\left(2t\right)=2\sin\left(t\right)co\sin\left(2t\right)=2\sin\left(t\right)c\sin\left(2t\right)=2\sin\left(t\right)\sin\left(2t\right)=2\sin\left(t\right)\sin\left(2t\right)=2\sin\left(\right)\sin\left(2t\right)=2\sin\sin\left(2t\right)=2si\sin\left(2t\right)=2s\sin\left(2t\right)=2\sin\left(2t\right)=\sin\left(2t\right)\sin\left(2t\right)\sin\left(2\right)\sin\left(\right)\sinsis

\cos\left(2t\right)=\cos^2\left(t\right)-\sin^2\left(t\right)=2\cos^2\left(t\right)-1=1-2\sin^2\left(t\right)\cos\left(2t\right)=\cos^2\left(t\right)-\sin^2\left(t\right)=2\cos^2\left(t\right)-1=1-2\sin^2\left(t\right)\cos\left(2t\right)=\cos^2\left(t\right)-\sin^2\left(t\right)=2\cos^2\left(t\right)-1=1-2\sin^2\left(\right)\cos\left(2t\right)=\cos^2\left(t\right)-\sin^2\left(t\right)=2\cos^2\left(t\right)-1=1-2\sin^2\cos\left(2t\right)=\cos^2\left(t\right)-\sin^2\left(t\right)=2\cos^2\left(t\right)-1=1-2\sin\cos\left(2t\right)=\cos^2\left(t\right)-\sin^2\left(t\right)=2\cos^2\left(t\right)-1=1-2si\cos\left(2t\right)=\cos^2\left(t\right)-\sin^2\left(t\right)=2\cos^2\left(t\right)-1=1-2s\cos\left(2t\right)=\cos^2\left(t\right)-\sin^2\left(t\right)=2\cos^2\left(t\right)-1=1-2\cos\left(2t\right)=\cos^2\left(t\right)-\sin^2\left(t\right)=2\cos^2\left(t\right)-1=1-\cos\left(2t\right)=\cos^2\left(t\right)-\sin^2\left(t\right)=2\cos^2\left(t\right)-1=1\cos\left(2t\right)=\cos^2\left(t\right)-\sin^2\left(t\right)=2\cos^2\left(t\right)-1=\cos\left(2t\right)=\cos^2\left(t\right)-\sin^2\left(t\right)=2\cos^2\left(t\right)-1\cos\left(2t\right)=\cos^2\left(t\right)-\sin^2\left(t\right)=2\cos^2\left(t\right)-\cos\left(2t\right)=\cos^2\left(t\right)-\sin^2\left(t\right)=2\cos^2\left(t\right)\cos\left(2t\right)=\cos^2\left(t\right)-\sin^2\left(t\right)=2\cos^2\left(t\right)\cos\left(2t\right)=\cos^2\left(t\right)-\sin^2\left(t\right)=2\cos^2\left(\right)\cos\left(2t\right)=\cos^2\left(t\right)-\sin^2\left(t\right)=2\cos^2\cos\left(2t\right)=\cos^2\left(t\right)-\sin^2\left(t\right)=2\cos\cos\left(2t\right)=\cos^2\left(t\right)-\sin^2\left(t\right)=2co\cos\left(2t\right)=\cos^2\left(t\right)-\sin^2\left(t\right)=2c\cos\left(2t\right)=\cos^2\left(t\right)-\sin^2\left(t\right)=2\cos\left(2t\right)=\cos^2\left(t\right)-\sin^2\left(t\right)=\cos\left(2t\right)=\cos^2\left(t\right)-\sin^2\left(t\right)\cos\left(2t\right)=\cos^2\left(t\right)-\sin^2\left(t\right)\cos\left(2t\right)=\cos^2\left(t\right)-\sin^2\left(\right)\cos\left(2t\right)=\cos^2\left(t\right)-\sin^2\cos\left(2t\right)=\cos^2\left(t\right)-\sin\cos\left(2t\right)=\cos^2\left(t\right)-si\cos\left(2t\right)=\cos^2\left(t\right)-s\cos\left(2t\right)=\cos^2\left(t\right)-\cos\left(2t\right)=\cos^2\left(t\right)\cos\left(2t\right)=\cos^2\left(t\right)-\cos\left(2t\right)=\cos^2\left(t\right)-\sin^{2\left(t\right)=2\cos^{}}\cos\left(2t\right)=\cos^2\left(t\right)-\sin^{2\left(t\right)=2\cos^2}\cos\left(2t\right)=\cos^2\left(t\right)-\sin^{2\left(t\right)=2\cos}\cos\left(2t\right)=\cos^2\left(t\right)-\sin^{2\left(t\right)=2co}\cos\left(2t\right)=\cos^2\left(t\right)-\sin^{2\left(t\right)=2c}\cos\left(2t\right)=\cos^2\left(t\right)-\sin^{2\left(t\right)=2}\cos\left(2t\right)=\cos^2\left(t\right)-\sin^{2\left(t\right)=}\cos\left(2t\right)=\cos^2\left(t\right)-\sin^{2\left(t\right)}\cos\left(2t\right)=\cos^2\left(t\right)-\sin^{2\left(t\right)}\cos\left(2t\right)=\cos^2\left(t\right)-\sin^{2\left(\right)}\cos\left(2t\right)=\cos^2\left(t\right)-\sin^2\cos\left(2t\right)=\cos^2\left(t\right)-\sin\cos\left(2t\right)=\cos^2\left(t\right)-si\cos\left(2t\right)=\cos^2\left(t\right)-s\cos\left(2t\right)=\cos^2\left(t\right)-\cos\left(2t\right)=\cos^2\left(t\right)\cos\left(2t\right)=\cos^2\left(t\right)\cos\left(2t\right)=\cos^2\left(\right)\cos\left(2t\right)=\cos^2\cos\left(2t\right)=\cos\cos\left(2t\right)=co\cos\left(2t\right)=c\cos\left(2t\right)=\cos\left(2t\right)\cos\left(2t\right)\cos\left(2\right)\cos\left(\right)\coscoc