document.write( "Question 39168: Sin w times Tan w + Cos w = Sec w \n" ); document.write( "
Algebra.Com's Answer #24602 by AnlytcPhil(1810) $\"\"$ $\"About$
You can put this solution on YOUR website!
Prove the identity\r\n" );
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document.write( "sin(w)·tan w + cos(w)        =      sec(w)\r\n" );
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document.write( "Simplify the more complicated side, the left\r\n" );
document.write( "Use the identity tanq = sinq/cosq\r\n" );
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document.write( "Replace tan(w) by sin(w)/cos(w)\r\n" );
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document.write( "       sin(w)\r\n" );
document.write( "sin(w)·—————— + cos(w)        =      sec(w)\r\n" );
document.write( "       cos(w)\r\n" );
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document.write( "       sin²(w)  cos(w)   \r\n" );
document.write( "      ——————— + ———————        =      sec(w)\r\n" );
document.write( "       cos(w)     1\r\n" );
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document.write( "Get the LCD = cos(w)\r\n" );
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document.write( "sin²(w)   cos(w)·cos(w)   \r\n" );
document.write( "——————— + —————————————        =      sec(w)\r\n" );
document.write( "cos(w)       1·cos(w)\r\n" );
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document.write( "sin²(w)      cos²(w)   \r\n" );
document.write( "——————— + —————————————        =      sec(w)\r\n" );
document.write( "cos(w)       cos(w)\r\n" );
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document.write( "Write over the LCD \r\n" );
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document.write( "sin²(w) +  cos²(w)   \r\n" );
document.write( "——————————————————             =      sec(w)\r\n" );
document.write( "     cos(w)  \r\n" );
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document.write( "Use identity sin²q + cos²q = 1\r\n" );
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document.write( "       1   \r\n" );
document.write( "    ———————                    =      sec(w)\r\n" );
document.write( "     cos(w)    \r\n" );
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document.write( "Use identity secq = 1/cosq\r\n" );
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document.write( "       sec(w)                  =      sec(w)\r\n" );
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document.write( "QED\r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com
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