document.write( "Question 747134: What are the x's of: ((cot^2)x) +(csc^2)x)) = 7 \n" ); document.write( "

Algebra.Com's Answer #454743 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"cot%28x%29=cos%28x%29%2Fsin%28x%29\"$ and $\"csc%28x%29=1%2Fsin%28x%29\"$ so
\n" ); document.write( " $\"%28cot%28x%29%29%5E2%2B%28csc%28x%29%29%5E2=7\"$ --> $\"%28cos%28x%29%29%5E2%2F%28sin%28x%29%29%5E2%2B1%2F%28sin%28x%29%29%5E2=7\"$
\n" ); document.write( "Multiplying both sides times $\"%28sin%28x%29%29%5E2\"$ we can eliminate denominators to get
\n" ); document.write( " $\"%28cos%28x%29%29%5E2%2B1=7%28sin%28x%29%29%5E2\"$ --> $\"1-%28sin%28x%29%29%5E2%2B1=7%28sin%28x%29%29%5E2\"$ --> $\"2-%28sin%28x%29%29%5E2=7%28sin%28x%29%29%5E2\"$ --> $\"2=8%28sin%28x%29%29%5E2\"$ --> $\"2%2F8=%28sin%28x%29%29%5E2\"$ --> $\"%28sin%28x%29%29%5E2=1%2F4\"$
\n" ); document.write( "The solutions must yield $\"sin%28x%29=1%2F2\"$ or $\"sin%28x%29=-1%2F2\"$
\n" ); document.write( "Looking for solution between $\"0%5Eo\"$ and $\"360%5Eo\"$ (between $\"0\"$ and $\"2pi\"$ radians),
\n" ); document.write( " $\"sin%28x%29=1%2F2\"$ happens for
\n" ); document.write( " $\"x=30%5Eo\"$ ( $\"pi%2F6\"$ radians) and $\"x=150%5Eo\"$ ( $\"5pi%2F6\"$ radians)
\n" ); document.write( "and $\"sin%28x%29=-1%2F2\"$ happens for
\n" ); document.write( " $\"x=210%5Eo\"$ ( $\"7pi%2F6\"$ radians) and $\"x=330%5Eo\"$ ( $\"11pi%2F6\"$ radians).
\n" ); document.write( "All solutions can be expressed as
\n" ); document.write( " $\"x=k%2A180%5Eo+%2B-+30%5Eo\"$ or $\"x=k%2Api+%2B-+pi%2F6\"$ \n" ); document.write( "

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