document.write( "Question 552116: Prove that
\n" ); document.write( "1 + tanAtanA/2 = tanAcotA/2 -1 = secA \n" ); document.write( "
Algebra.Com's Answer #360184 by AnlytcPhil(1810)\"\" \"About 
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document.write( "1 + tan(A)·tan\"%28A%2F2%29\" = tan(A)cot\"%28A%2F2%29\" - 1 = sec(A)\r\n" );
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document.write( "We will make use of the half angle identities:\r\n" );
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document.write( "tan\"%28A%2F2%29\" = \"%281-cos%28A%29%29%2Fsin%28A%29\", and its reciprocal cot\"%28A%2F2%29\" = \"sin%28A%29%2F%281-cos%28A%29%29\", also tan(A) = \"sin%28A%29%2Fcos%28A%29\" and sec(A) = \"1%2Fcos%28A%29\"\r\n" );
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document.write( "First we will prove:\r\n" );
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document.write( "1 + tan(A)·tan\"%28A%2F2%29\" = sec(A)\r\n" );
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document.write( "1 + \"%28sin%28A%29%2Fcos%28A%29%29\"\"%28%281-cos%28A%29%29%2Fsin%28A%29%29\" \r\n" );
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document.write( "1 + \"+++%28sin%28A%29-sin%28A%29cos%28A%29%29++%2F%28cos%28A%29sin%28A%29%29+++\"\r\n" );
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document.write( "Get an LCD\r\n" );
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document.write( "\"%28cos%28A%29sin%28A%29%29%2F%28cos%28A%29sin%28A%29%29\" + \"+++%28sin%28A%29-sin%28A%29cos%28A%29%29++%2F%28cos%28A%29sin%28A%29%29+++\"\r\n" );
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document.write( "Combine fractions over the LCD\r\n" );
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document.write( "Cancel first and third terms on top:\r\n" );
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document.write( "\"sin%28A%29++%2F%28cos%28A%29sin%28A%29%29+++\"\r\n" );
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document.write( "Cancel the sines:\r\n" );
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document.write( "\"cross%28sin%28A%29%29++%2F%28cos%28A%29cross%28sin%28A%29%29%29+++\"\r\n" );
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document.write( "\"1%2Fcos%28A%29\"\r\n" );
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document.write( "sec(A)\r\n" );
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document.write( "---------------------------------\r\n" );
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document.write( "Next we will prove:\r\n" );
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document.write( "tan(A)·cot\"%28A%2F2%29\" - 1 = sec(A)\r\n" );
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document.write( "\"%28sin%28A%29%2Fcos%28A%29%29\"\"%28sin%28A%29%2F%281-cos%28A%29%29%29\" - 1 \r\n" );
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document.write( "\"+++%28sin%5E2%28A%29%29++%2F%28cos%28A%29%281-cos%28A%29%29%29+++\" - 1\r\n" );
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document.write( "Get an LCD\r\n" );
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document.write( "\"+++%28sin%5E2%28A%29%29++%2F%28cos%28A%29%281-cos%28A%29%29%29+++\" - \"+++%28cos%28A%29%281-cos%28A%29%29%29++%2F%28cos%28A%29%281-cos%28A%29%29%29+++\"\r\n" );
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document.write( "Combine fractions over the LCD\r\n" );
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document.write( "Distribute:\r\n" );
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document.write( "Rearrange:\r\n" );
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document.write( "Use identity sin²(A)+cos²(A)=1\r\n" );
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document.write( "\"+++%281-cos%28A%29%29++%2F%28cos%28A%29%281-cos%28A%29%29%29+++\"\r\n" );
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document.write( "Cancel 1-cos(A)'s\r\n" );
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document.write( "\"+++%28cross%281-cos%28A%29%29%29++%2F%28cos%28A%29%28cross%281-cos%28A%29%29%29%29+++\"\r\n" );
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document.write( "\"1%2Fcos%28A%29\"\r\n" );
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document.write( "sec(A)\r\n" );
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document.write( "Edwin
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