Question 40967
Using a trig identity,
log (cot^2 x + 1) =
log (csc^2 x) =
log (1 / sin^2 x)
Now if log sin x = a
sin x = 10^a (in base 10) and
sin^2 x = 10^2a so that
log (1 / sin^2 x) =
log (10^(-2a)) = 
-2a