document.write( "Question 1201965: prove that -sin(x)-cos(x)cot(x)=-csc(x) is an identity \n" ); document.write( "

Algebra.Com's Answer #836566 by Theo(13342) $\"\"$ $\"About$

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equation is:
\n" ); document.write( "-sin(x) - cos(x) * cot(x) = -csc(x)
\n" ); document.write( "csc(x) = 1/sin(x)
\n" ); document.write( "cot(x) = cos(x) / sin(x)
\n" ); document.write( "equation becomes:
\n" ); document.write( "-sin(x) - cos(x) * cos(x) / sin(x) = -1/sin(x)
\n" ); document.write( "multiply both sides of the equation by sin(x) to get:
\n" ); document.write( "-sin^2(x) - cos^2(x) = -1
\n" ); document.write( "factor the left side of the equation by -1 to get:
\n" ); document.write( "-1 * (sin^2(x) + cos^2(x) = -1
\n" ); document.write( "since sin^2(x) + cos^(x) = 1, you get:
\n" ); document.write( "-1 = -1.
\n" ); document.write( "this confirms the identity is correct.
\n" ); document.write( " \n" ); document.write( "

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