Archive
7th of September 2015
Mathematics
Q:

if tan A = n tan B and sin A = m sin B, PROVE THAT COS SQUARE A = m2 - 1 / n2 - 1

Nisha_vini29 - Junior - Class VI

Monday, September 07, 2015 at 18:21:PM

A:

fraction numerator t a n A over denominator t a n B end fraction equals n fraction numerator s i n A c o s B over denominator c o s A s i n B end fraction equals n..... left parenthesis i right parenthesis  fraction numerator s i n A over denominator s i n B end fraction equals m s i n A space equals space m space s i n B  f r o m left parenthesis i right parenthesis therefore fraction numerator c o s B over denominator c o s A end fraction equals n over m m c o s B equals n c o s A  n squared c o s squared A equals m squared c o s squared B space space space space space space space space space space space space space space equals m squared open parentheses 1 minus s i n squared B close parentheses space space space space space space space space space space space space space space space space equals m squared open parentheses 1 minus fraction numerator s i n squared A over denominator m squared end fraction close parentheses space space space space space space space space space space space space space space space space space equals m squared minus s i n squared A space space space space space space space space space space space space space space space space space equals m squared minus 1 plus c o s squared A therefore n squared c o s squared A minus c o s squared A equals m squared minus 1  therefore c o s squared A equals fraction numerator m squared minus 1 over denominator n squared minus 1 end fraction

Monday, September 07, 2015 at 18:34:PM