SOLUTION: If log sin x = a and log cos x = b, then log (cot ^2 x + 1) = ?

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Question 40967: If log sin x = a and log cos x = b, then log (cot ^2 x + 1) = ?
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
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