CBSE Class 11-science Answered

The expression S=sec11°.sec19°-2cot71° reduces to?

Asked by ajayagarwal1970 | 06 Jul, 2014, 11:53: PM

Expert Answer

$S equals s e c space 11 space s e c space 19 space minus space 2 space c o t space 71 S equals fraction numerator 1 over denominator cos space 11 space cos space 19 end fraction minus 2 open parentheses fraction numerator cos space 71 over denominator sin space 71 end fraction close parentheses equals fraction numerator 1 over denominator cos space 11 space sin space 71 end fraction minus 2 open parentheses fraction numerator cos space 71 over denominator sin space 71 end fraction close parentheses S equals fraction numerator 1 minus 2 cos space 71 space cos space 11 over denominator cos space 11 space sin space 71 end fraction S equals fraction numerator 1 minus 2 cos open parentheses 60 plus 11 close parentheses cos space 11 over denominator cos space 11 space sin space 71 end fraction cos open parentheses 60 plus 11 close parentheses equals cos space 60 space cos space 11 space minus space sin space 60 space sin space 11 equals 1 half open parentheses cos space 11 minus square root of 3 space sin space 11 close parentheses S equals fraction numerator 1 minus open parentheses cos space 11 minus square root of 3 space sin space 11 close parentheses cos space 11 over denominator cos space 11 space sin space 71 end fraction S equals fraction numerator 1 minus cos squared space 11 space plus thin space square root of 3 sin space 11 space cos space 11 over denominator open parentheses cos space 11 space sin space 71 close parentheses end fraction S equals fraction numerator sin squared space 11 plus square root of 3 sin 11 space cos space 11 over denominator cos space 11 space sin space 71 end fraction S equals fraction numerator sin space 11 over denominator cos space 11 end fraction open parentheses fraction numerator sin 11 plus square root of 3 cos space 11 over denominator sin space 71 end fraction close parentheses M u l t i p l y i n g space a n d space d i v i d i n g space a b o v e space e q u a t i o n space b y space 2 comma space w e space g e t S equals 2 space T a n space 11 fraction numerator open parentheses begin display style 1 half end style sin 11 plus begin display style fraction numerator square root of 3 over denominator 2 end fraction end style cos space 11 close parentheses over denominator sin space 71 end fraction S equals 2 space T a n space 11 space fraction numerator sin left parenthesis 60 plus 11 right parenthesis over denominator sin space 71 end fraction equals 2 space T a n space 11$