document.write( "Question 735446: How to verify the identity of sin x / 1 - cos x \n" ); document.write( "

Algebra.Com's Answer #449452 by fcabanski(1391) $\"\"$ $\"About$

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Multiply by the conjugate of the denominator over itself. The conjugate of a+b is a-b. Any value over itself = 1. So you're just multiplying by one and thus keeping the same value.

\n" ); document.write( "sin x / (1 - cos x) * (1+cos x) / (1+cos x) = sin x(1+cos x)/ (1-cos x)(1+cos x) = sin x(1+cos x)/ 1 - cos^2 x

\n" ); document.write( "Remember that sin^2 x + cos^2 x = 1 and thus 1-cos^2 x = sin^2 x

\n" ); document.write( "sin x(1+cos x)/ 1 - cos^2 x = sin x (1+cos x) / sin^2 x = (1+cos x) / sin x
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Hope the solution helped. Sometimes you need more than a solution. Contact fcabanski@hotmail.com for online, private tutoring, or personalized problem solving (quick for groups of problems.) \n" ); document.write( "

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