(cosA-sinA+1)      (1+cosA)
Prove that    ---------------   =  ---------
                    (cosA+sinA-1)        (sinA)
 
pls someone help urgently

Asked by Aayushi Grover | 5th Sep, 2014, 11:39: AM

Expert Answer:

fraction numerator left parenthesis cos space A minus sin space A plus 1 right parenthesis over denominator left parenthesis cos space A plus sin space A minus 1 right parenthesis end fraction equals fraction numerator left parenthesis 1 plus cos space A right parenthesis over denominator sin space A end fraction L H S comma fraction numerator left parenthesis cos space A minus sin space A plus 1 right parenthesis left parenthesis cos space A plus sin space A plus 1 right parenthesis over denominator left parenthesis cos space A plus sin space A minus 1 right parenthesis left parenthesis cos space A plus sin space A plus 1 right parenthesis end fraction space left square bracket R a t i o n a l i z i n g space t h e space d e n o m i n a t o r right square bracket equals fraction numerator left parenthesis cos space A plus 1 minus sin space A right parenthesis left parenthesis cos space A plus 1 plus sin space A right parenthesis over denominator left parenthesis cos space A plus sin space A right parenthesis squared minus 1 end fraction equals fraction numerator left parenthesis cos space A plus 1 right parenthesis squared minus sin squared A over denominator left parenthesis cos space A plus sin space A right parenthesis squared minus 1 end fraction equals fraction numerator cos squared A plus 1 plus 2 space cos space A minus sin squared A over denominator cos squared A plus sin squared A plus 2 space sin space A cos space A minus 1 end fraction equals fraction numerator cos squared A plus 2 space cos space A plus 1 minus sin squared A over denominator cos squared A plus sin squared A minus 1 plus 2 space sin space A space cos space A end fraction equals fraction numerator cos squared A plus 2 space cos space A plus cos squared A over denominator 1 minus 1 plus 2 space sin space A space cos space A end fraction left square bracket because cos squared A plus sin squared A equals 1 right square bracket equals fraction numerator 2 cos squared A plus 2 space cos space A over denominator 2 space sin space A space cos space A end fraction equals fraction numerator 2 space cos space A left parenthesis 1 plus cos space A right parenthesis over denominator 2 space sin space A cos space A end fraction equals fraction numerator 1 plus cos space A over denominator sin space A end fraction equals R H S

Answered by Prasenjit Paul | 8th Sep, 2014, 10:36: AM