document.write( "Question 1037392: Use a sum or difference formula to write a formula for cos⁡2x. Express the result in terms of sin⁡x and cos⁡x. \n" ); document.write( "

Algebra.Com's Answer #652038 by ikleyn(52787) $\"\"$ $\"About$

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\n" ); document.write( "1. Use a sum or difference formula to write a formula for cos(2x).
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document.write( "1.  The \"addition formula\" for cosine is \r\n" );
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document.write( "    cos(x+y) = cos(x)*cos(y) - sin(x)*sin(y)\r\n" );
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document.write( "    (see the lesson Addition and subtraction formulas in this site.)\r\n" );
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document.write( "    Take x = y in this formula, and you will get \r\n" );
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document.write( "    cos(2x) = .   (1)\r\n" );
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document.write( "    It is the answer for #1.\r\n" );
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document.write( "2.  You can express (1) in terms of sin(x) only.\r\n" );
document.write( "    For it, substitute  cos^2(x) = 1 - sin^2(x)  into (1).  You will get\r\n" );
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document.write( "    cos(2x) = .   (2)\r\n" );
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document.write( "    Or,  you can express (1) in terms of cos(x) only.\r\n" );
document.write( "    For it, substitute  sin^2(x) = 1 - cos^2(x)  into (1).  You will get\r\n" );
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document.write( "    cos(2x) = .   (3)\r\n" );
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