document.write( "Question 826390: Prove using reciprocal and pythagorean identities: (cscx-cotx)/(secx-1)= cotx
\n" ); document.write( "I have already done:
\n" ); document.write( "((1/sinx)-(cosx/sinx))/((1/cosx)-1))=
\n" ); document.write( "((1-cosx)/sinx))/((1-cosx)/(cosx))=
\n" ); document.write( "((1-cosx)/sinx))*((cosx)/(1-cosx))=
\n" ); document.write( "((1-cosx)cosx))/((sinx(1-cosx))=
\n" ); document.write( "((cosx-(cos^2))/(sinx-sinxcosx)
\n" ); document.write( "This is where is get stuck...
\n" ); document.write( "Thank you \n" ); document.write( "

Algebra.Com's Answer #498163 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
You're going to laugh (or cry) when you see how close you were:
\n" ); document.write( " $\"%28cos%28x%29-cos%5E2%28x%29%29%2F%28sin%28x%29-sin%28x%29cos%28x%29%29\"$
\n" ); document.write( "We're going to reduce this fraction. And since only factors cancel, we will factor the numerator and denominator:
\n" ); document.write( " $\"%28cos%28x%29%281-cos%28x%29%29%29%2F%28sin%28x%29%281-cos%28x%29%29%29\"$
\n" ); document.write( "And, as we can see, a factor will cancel:
\n" ); document.write( "

\n" ); document.write( "leaving
\n" ); document.write( " $\"cos%28x%29%2Fsin%28x%29\"$
\n" ); document.write( "which is equal to:
\n" ); document.write( " $\"cot%28x%29\"$ \n" ); document.write( "

\n" );