document.write( "Question 40967: If log sin x = a and log cos x = b, then log (cot ^2 x + 1) = ? \n" ); document.write( "

Algebra.Com's Answer #26406 by fractalier(6550) $\"\"$ $\"About$

You can put this solution on YOUR website!
Using a trig identity,
\n" ); document.write( "log (cot^2 x + 1) =
\n" ); document.write( "log (csc^2 x) =
\n" ); document.write( "log (1 / sin^2 x)
\n" ); document.write( "Now if log sin x = a
\n" ); document.write( "sin x = 10^a (in base 10) and
\n" ); document.write( "sin^2 x = 10^2a so that
\n" ); document.write( "log (1 / sin^2 x) =
\n" ); document.write( "log (10^(-2a)) =
\n" ); document.write( "-2a \n" ); document.write( "

\n" );