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Q:Write into simplest form
                                 c o t to the power of negative 1 end exponent left parenthesis square root of 1 plus x squared end root minus x right parenthesis .

Asked by Ravi consul 15th March 2015, 8:20 PM
Answered by Expert
Answer:
l e t space x equals space tan space theta theta equals tan to the power of negative 1 end exponent x comma c o t to the power of negative 1 end exponent open parentheses square root of 1 plus x squared end root minus x close parentheses equals c o t to the power of negative 1 end exponent open parentheses square root of 1 plus tan squared theta end root minus tan space theta close parentheses equals c o t to the power of negative 1 end exponent open parentheses s e c space theta minus tan space theta close parentheses equals c o t to the power of negative 1 end exponent open parentheses fraction numerator 1 over denominator cos space theta end fraction minus fraction numerator sin space theta over denominator cos space theta end fraction close parentheses equals c o t to the power of negative 1 end exponent open parentheses fraction numerator 1 minus sin space theta over denominator cos space theta end fraction close parentheses equals tan to the power of negative 1 end exponent open parentheses fraction numerator cos space theta over denominator 1 minus sin space theta end fraction close parentheses equals tan to the power of negative 1 end exponent open parentheses fraction numerator cos space squared begin display style theta over 2 end style minus sin squared begin display style theta over 2 end style over denominator cos squared begin display style theta over 2 end style plus sin squared begin display style theta over 2 end style minus 2 sin begin display style theta over 2 end style cos begin display style theta over 2 end style end fraction close parentheses equals tan to the power of negative 1 end exponent open parentheses fraction numerator begin display style open parentheses cos theta over 2 minus sin theta over 2 close parentheses open parentheses cos theta over 2 plus sin theta over 2 close parentheses end style over denominator begin display style open parentheses cos theta over 2 minus sin theta over 2 close parentheses squared end style end fraction close parentheses equals tan to the power of negative 1 end exponent open parentheses fraction numerator begin display style open parentheses cos theta over 2 plus sin theta over 2 close parentheses end style over denominator begin display style open parentheses cos theta over 2 minus sin theta over 2 close parentheses end style end fraction close parentheses equals tan to the power of negative 1 end exponent open parentheses fraction numerator begin display style bevelled fraction numerator begin display style open parentheses cos theta over 2 plus sin theta over 2 close parentheses end style over denominator cos space begin display style theta over 2 end style end fraction end style over denominator begin display style bevelled fraction numerator begin display style open parentheses cos theta over 2 minus sin theta over 2 close parentheses end style over denominator cos space begin display style theta over 2 end style end fraction end style end fraction close parentheses equals tan to the power of negative 1 end exponent open parentheses fraction numerator begin display style open parentheses 1 plus tan theta over 2 close parentheses end style over denominator begin display style open parentheses 1 minus tan theta over 2 close parentheses end style end fraction close parentheses equals tan to the power of negative 1 end exponent open parentheses fraction numerator begin display style open parentheses tan space straight pi over 4 plus tan theta over 2 close parentheses end style over denominator begin display style open parentheses 1 minus tan space straight pi over 4. tan theta over 2 close parentheses end style end fraction close parentheses equals tan to the power of negative 1 end exponent open parentheses tan open parentheses straight pi over 4 plus theta over 2 close parentheses close parentheses space space space open square brackets S i n c e comma space tan to the power of negative 1 end exponent open parentheses tan space theta close parentheses equals theta close square brackets equals straight pi over 4 plus fraction numerator tan to the power of negative 1 end exponent x over denominator 2 end fraction
Answered by Expert 16th March 2015, 12:32 PM
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