document.write( "Question 451411: Simplify completely\r
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Algebra.Com's Answer #310386 by kingme18(98) $\"\"$ $\"About$

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The top is a difference of two squares. Remember that $\"+a%5E2-b%5E2=%28a%2Bb%29%28a-b%29+\"$ In your case, a is cos(x)+sin(x), and b is cos(x)-sin(x). Substitute those in and the first parentheses is $\"+%28cos%28x%29%2Bsin%28x%29+%2B+cos%28x%29-sin%28x%29%29+\"$ , which simplifies to 2cos(x). For the other, don't forget to distribute the subtraction: $\"+cos%28x%29%2Bsin%28x%29-%28cos%28x%29-sin%28x%29%29+\"$ , which simplifies to 2sin(x). Thus, at this point we have: $\"+%282cos%28x%29%2A2sin%28x%29%29%2F%282sin%282x%29%29+\"$ .\r
\n" ); document.write( "\n" ); document.write( "The double angle formula for sine says $\"+sin%282x%29+=+2sin%28x%29cos%28x%29+\"$ . The denominator is then $\"+2%2A2sin%28x%29cos%28x%29+\"$ . If we simplify the numerator and denominator, we have $\"+%284sin%28x%29cos%28x%29%29%2F%284sin%28x%29cos%28x%29%29+\"$ , which is, of course, 1 :) \n" ); document.write( "

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