document.write( "Question 1142320: Prove that
\n" ); document.write( "[ 1 + sin(2x)] / [ 1 + cos(2x)] = 1/2 (1+ tan(x))^2 \n" ); document.write( "

Algebra.Com's Answer #763078 by math_helper(2461) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "LHS:
\n" ); document.write( " $\"+%28+1+%2B+sin%282x%29%29+%2F+%28+1+%2B+cos%282x%29%29+\"$
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\n" ); document.write( "\n" ); document.write( "Use $\"+1%2Bsin%282x%29+=+1%2B2sin%28x%29cos%28x%29+\"$ and $\"+cos%282x%29+=+cos%5E2%28x%29-sin%5E2%28x%29\"$ :

\n" ); document.write( " = $\"+%28+1+%2B+2%2Asin%28x%29cos%28x%29%29+%2F+%28+1+%2B+cos%5E2%28x%29+-+sin%5E2%28x%29%29+\"$

\n" ); document.write( " = $\"+%28+1+%2B+2%2Asin%28x%29cos%28x%29%29+%2F+%28+2%2Acos%5E2%28x%29%29+\"$

\n" ); document.write( " = $\"+%281%2F2%29+%28%281%2Fcos%5E2%28x%29%29+%2B+2%2A%28sin%28x%29%2Fcos%28x%29%29%29+\"$

\n" ); document.write( " = $\"+%281%2F2%29+%28+sec%5E2%28x%29+%2B+2tan%28x%29%29+\"$

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\n" ); document.write( "\n" ); document.write( "RHS:
\n" ); document.write( " $\"+%281%2F2%29+%281%2B+tan%28x%29%29%5E2++\"$
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\n" ); document.write( "\n" ); document.write( "Expand:
\n" ); document.write( " = $\"++%281%2F2%29+%281+%2B+2tan%28x%29+%2B+tan%5E2%28x%29%29+\"$
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\n" ); document.write( "\n" ); document.write( "Use: $\"+1%2Btan%5E2%28x%29+=+sec%5E2%28x%29+\"$ :
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\n" ); document.write( "\n" ); document.write( " = $\"+%281%2F2%29+%28sec%5E2%28x%29+%2B+2tan%28x%29%29+\"$ \r
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\n" ); document.write( "\n" ); document.write( "The LHS and RHS are both equal to $\"+%281%2F2%29+%28sec%5E2%28x%29+%2B+2tan%28x%29%29+\"$ and hence they are both equal to each other.\r
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