show that cotA-cosA/cotA+cosA=cosecA-1/cosecA+1

Asked by prabinbinu2001 | 25th Sep, 2016, 03:26: PM

Expert Answer:

begin mathsize 20px style W e space k n o w space t h a t space C o t A equals fraction numerator C o s space A over denominator S i n A end fraction
S u b s i t u t e space t h e space v a l u e space o f space C o t A equals fraction numerator C o s space A over denominator S i n A end fraction space i n space t h e space L H S space o f space t h e space g i v e n space E q u a t i o n
W e space g e t comma
fraction numerator C o t space A space minus space C o s space A over denominator C o t space A space plus space C o s A end fraction equals space fraction numerator fraction numerator C o s space A over denominator S i n A end fraction minus C o s space A over denominator fraction numerator C o s space A over denominator S i n A end fraction plus C o s space A end fraction equals fraction numerator C o s space A open parentheses begin display style fraction numerator 1 over denominator S i n space A end fraction end style minus 1 close parentheses over denominator C o s space A open parentheses fraction numerator 1 over denominator S i n space A end fraction plus 1 close parentheses end fraction space space open square brackets T a k i n g space C o s space A space c o m m o n space f r o m space b o t h space t h e space s i d e s close square brackets
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space fraction numerator open parentheses fraction numerator 1 over denominator S i n space A end fraction minus 1 close parentheses over denominator open parentheses fraction numerator 1 over denominator S i n space A end fraction plus 1 close parentheses end fraction space space space open square brackets C a n c e l l i n g space C o s space A space f r o m space b o t h space t h e space s i d e s close square brackets
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator cos e c space A minus 1 space over denominator cos e c space A plus 1 end fraction space space space open square brackets fraction numerator 1 over denominator S i n space A end fraction equals C o s e c A close square brackets
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space R H S
H e n c e space L H S space equals space R H S
end style

Answered by Tripti Agrawal | 26th Sep, 2016, 11:34: AM