Law of cosine in spherical trigonometry

Question

I found from a book of mine the formula $\cos a=\cos b\cos c+\sin b\sin c\cos\alpha.$ Can this be true? If for example $a=1m,b=1m,c=1m,\alpha=1$, $m$ denotes by meter, then $\cos m=\cos^2 m+\sin^2m\cos 1.$ There seems to be some mistake in units if cosine meters are sum of cosine square meters and sine square meters.