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A man walking briskly in rain with speed...

A man walking briskly in rain with speed v must slant his umbrella forward making an angle `theta` with the vertical. A student derives the following relation between `theta` and v : tan `theta` = v and checks that the relation has a correct limit: as `v rarr 0`, `theta rarr o`, as expected. (We are assuming there is no strong wind and that the rain falls vertically for a stationary man). Do you think this relation can be correct ? If not, guess the correct relation.

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Prove the following identity : 1/(sec theta-tan theta)= (1+sin theta)/(cos theta) = sec theta+tan theta .

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