{"result":{"text":"square root of 1 plus sin x end root equals square root of open parentheses cos x over 2 plus sin x over 2 close parentheses squared end root equals cos x over 2 plus sin x over 2\nA l s o comma space space square root of 1 minus sin x end root equals square root of open parentheses cos fraction numerator begin display style x end style over denominator begin display style 2 end style end fraction minus sin fraction numerator begin display style x end style over denominator begin display style 2 end style end fraction close parentheses squared end root equals cos fraction numerator begin display style x end style over denominator begin display style 2 end style end fraction minus sin fraction numerator begin display style x end style over denominator begin display style 2 end style end fraction space\nN o w comma space y equals fraction numerator 2 cos x over 2 over denominator negative 2 sin x over 2 end fraction equals negative cot x over 2 rightwards double arrow fraction numerator d y over denominator d x end fraction equals 1 half cosec squared fraction numerator begin display style x end style over denominator begin display style 2 end style end fraction"},"status":"ok"}