Question

Solve:

(1/sin 45 sin 46)+ (1/sin 47 sin 48)+......... (1/ sin 133 sin 134)

Answer 1

\[\frac{1}{\sin 45 * \sin 46}+\frac{1}{\sin 47 * \sin 48}+...+\frac{1}{\sin 131*\sin132}+\frac{1}{\sin 133 * \sin 134}\]
is that basically what you're after?

Answer 2

Yeah

Answer 3

I'm not entirely sure how to approach this one.
Generally, you can add like the last term and the first and that will be the same as the 2nd and the next to last and so on... but that doesnt work here.
In decimal notation,
1.96599+1.83992+...+1.78298+1.90081
converting to cosines offers something almost useful, but I cant see any type of recursion in any of these.