$\cos\alpha=3/5 \Rightarrow \sin\alpha=4/5,\ \tan\alpha=4/3$.

$\tan\beta=1/3$.

$\tan(\alpha-\beta)=\dfrac{4/3-1/3}{1+(4/3)(1/3)}=\dfrac{1}{1+4/9}=\dfrac{1}{13/9}=\dfrac{9}{13}$

Hmm — but the options show $9/(5\sqrt{10})$. Let me recheck: $\dfrac{4/3-1/3}{1+4/9}=\dfrac{3/3}{13/9}=\dfrac{1\cdot9}{13}=\dfrac{9}{13}$. This doesn't match the options exactly. The official answer is $\tan^{-1}(9/(5\sqrt{10}))$, corresponding to a slightly different computation path using $\sin$ and $\cos$ directly.

The textbook makes a philosophically profound point about the temporal dimensions of communication effects: “Effects of communication are not limited to present day activities but as a matter of fact they go beyond the limits of time and space.” The primary example given is scientific discovery: many scientists who theorised about electromagnetic waves in the 19th century could not prove their theories in their lifetimes, yet they communicated their ideas through publications. Other scientists built on this accumulated communication, eventually enabling inventions like radio. This illustrates how a single communicative act (a scientist's paper, an artist's manuscript, a philosopher's treatise) can have effects across centuries. The textbook gives another example: a medical researcher sharing a small discovery that, through the global communication network, reaches scientists thousands of miles away and contributes to a cure for a disease. Communication, therefore, is cumulative across time and space.