document.write( "Question 1206383: Prove the identity
\n" ); document.write( "i) cotx - cot2x = cosec2x
\n" ); document.write( "ii) Show that *integral* (with limit pi/4 and pi/6) cot x dx = 1/2 ln 2.
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Algebra.Com's Answer #843813 by AnlytcPhil(1807)\"\" \"About 
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document.write( "iii) Find the exact value of *integral* (with limit pi/4 and pi/6) cosec 2x dx, giving your answer in the form alnb.\r\n" );
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document.write( "Use the formula:\r\n" );
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document.write( "\"int%28cosec%28u%5E%22%22%29%2Cdu%29\"\"%22%22=%22%22\"\"ln%28tan%5E%22%22%28u%2F2%29%5E%22%22%5E%22%22%29%2B+C\"\r\n" );
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document.write( "\"int%28cosec%282x%29%2Cdx%2Cpi%2F6%2Cpi%2F4%29\"\"%22%22=%22%22\"\"expr%281%2F2%29int%28cosec%282x%29%2C%282dx%29%2Cpi%2F6%2Cpi%2F4%29\"\"%22%22=%22%22\"\"expr%281%2F2%29ln%28tan%5E%22%22%282x%2F2%29%5E%22%22%5E%22%22%29\"\"%22%22=%22%22\"\"expr%281%2F2%29ln%28tan%5E%22%22%28x%29%5E%22%22%5E%22%22%29\"\"%22%22=%22%22\"\"%22%22=%22%22\"\"expr%281%2F2%29%28ln%281%5E%22%22%29-ln%28sqrt%283%29%2F3%29%5E%22%22%29\"\"%22%22=%22%22\"\"expr%281%2F2%29%280-ln%28sqrt%283%29%2F3%29%5E%22%22%29\"\"%22%22=%22%22\"\r\n" );
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document.write( "\"expr%28-1%2F2%29ln%28sqrt%283%29%2F3%29\"\"%22%22=%22%22\"\"-expr%281%2F2%29%28ln%28sqrt%283%29%29-ln%283%5E%22%22%29%5E%22%22%29\"\"%22%22=%22%22\"\"%22%22=%22%22\"\"expr%28-1%2F2%29%28expr%281%2F2%29ln%283%5E%22%22%29-ln%283%5E%22%22%29%5E%22%22%29\"\"%22%22=%22%22\"\"expr%28-1%2F2%29%28-expr%281%2F2%29ln%283%5E%22%22%29%5E%22%22%29\"\"%22%22=%22%22\"\"expr%281%2F4%29ln%283%5E%22%22%29\"\r\n" );
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document.write( "Edwin
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