document.write( "Question 1204327: If sin 𝛼 + sin 𝛽 = 𝑝, cos 𝛼 − cos 𝛽 = 𝑞, where 𝑝 ≠ 0 and 𝑝 ≠ 𝑞, find cot(𝛼 − 𝛽) in terms of 𝑝 and 𝑞. \n" ); document.write( "
Algebra.Com's Answer #840592 by Edwin McCravy(20065)\"\" \"About 
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If sin 𝛼 + sin 𝛽 = 𝑝, cos 𝛼 − cos 𝛽 = 𝑞, where 𝑝 ≠ 0 and 𝑝 ≠ 𝑞,
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document.write( "We use the sum/difference to product trig identities:\r\n" );
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document.write( "\"p\"\"%22%22=%22%22\"\"sin%28alpha%29%2Bsin%28beta%29\"\"%22%22=%22%22\"\"2sin%28expr%281%2F2%29%28alpha%2Bbeta%29%29%2Acos%28expr%281%2F2%29%28alpha-beta%29%29\"\r\n" );
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document.write( "\"q\"\"%22%22=%22%22\"\"cos%28alpha%29-cos%28beta%29\"\"%22%22=%22%22\"\"-2sin%28expr%281%2F2%29%28alpha%2Bbeta%29%29%2Asin%28expr%281%2F2%29%28alpha-beta%29%29\"\r\n" );
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document.write( "\"p%2Fq\"\"%22%22=%22%22\"\"%22%22=%22%22\"\"-cos%28expr%281%2F2%29%28alpha-beta%29%29%2Fsin%28expr%281%2F2%29%28alpha-beta%29%29\"\"%22%22=%22%22\"\"-cot%28expr%281%2F2%29%28alpha-beta%29%29\"\r\n" );
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document.write( "\"cot%28expr%281%2F2%29%28alpha-beta%29%29\"\"%22%22=%22%22\"\"-p%2Fq\"\r\n" );
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document.write( "We use the trig identity \"cot%282%2Aphi%29\"\"%22%22=%22%22\"\"%28cot%5E2%28phi%29-1%29%2F%282%2Acot%5E%22%22%28phi%29%29\" with \"phi\"\"%22%22=%22%22\"\"expr%281%2F2%29%28alpha-beta%29\"\r\n" );
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document.write( "\"cot%5E%22%22%28alpha-beta%29\"\"%22%22=%22%22\"\"cot%282%2Aexpr%281%2F2%29%28alpha-beta%29%29\"\"%22%22=%22%22\"\"%28%28-p%2Fq%29%5E2-1%29%2F%282%2A%28-p%2Fq%29%29\"\"%22%22=%22%22\"\"-%28p%5E2%2Fq%5E2-1%29%2F%282p%5E%22%22%2Fq%5E%22%22%29\"\r\n" );
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document.write( "Multiply top and bottom by q2:\r\n" );
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document.write( "\"cot%5E%22%22%28alpha-beta%29\"\"%22%22=%22%22\"\"-%28p%5E2-q%5E2%29%2F%282pq%5E%22%22%29\"\"%22%22=%22%22\"\"%28q%5E2-p%5E2%29%2F%282pq%5E%22%22%29\"\r\n" );
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document.write( "Edwin
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