sir, prove that : if tanA=n.tanB  & sinA=m.sinB  prove that cos square A =m square -1 by n square -1

Asked by 61neethu | 8th Aug, 2015, 06:07: PM

Expert Answer:

G i v e n space t h a t space tan A equals n cross times tan B space a n d space sin A equals m cross times sin B rightwards double arrow n equals fraction numerator tan A over denominator tan B end fraction space a n d space m equals fraction numerator sin A over denominator sin B end fraction N o w space c o n s i d e r comma fraction numerator m squared minus 1 over denominator n squared minus 1 end fraction equals fraction numerator open parentheses fraction numerator sin A over denominator sin B end fraction close parentheses squared minus 1 over denominator open parentheses fraction numerator tan A over denominator tan B end fraction close parentheses squared minus 1 end fraction space space space space space space space space space space space space equals fraction numerator open parentheses fraction numerator s i n squared A over denominator s i n squared B end fraction close parentheses minus 1 over denominator open parentheses fraction numerator t a n squared A over denominator t a n squared B end fraction close parentheses minus 1 end fraction space space space space space space space space space space space space equals fraction numerator open parentheses fraction numerator s i n squared A minus s i n squared B over denominator s i n squared B end fraction close parentheses over denominator open parentheses fraction numerator t a n squared A minus t a n squared B over denominator t a n squared B end fraction close parentheses end fraction space space space space space space space space space space space space equals fraction numerator s i n squared A minus s i n squared B over denominator s i n squared B end fraction cross times fraction numerator t a n squared B over denominator t a n squared A minus t a n squared B end fraction space space space space space space space space space space space space equals fraction numerator s i n squared A minus s i n squared B over denominator s i n squared B end fraction cross times fraction numerator begin display style fraction numerator s i n squared B over denominator cos squared B end fraction end style over denominator begin display style fraction numerator sin squared A over denominator cos squared A end fraction end style minus fraction numerator s i n squared B over denominator c o s squared B end fraction end fraction space space space space space space space space space space space space equals fraction numerator s i n squared A minus s i n squared B over denominator s i n squared B end fraction cross times fraction numerator begin display style fraction numerator s i n squared B over denominator c o s squared B end fraction end style over denominator begin display style fraction numerator s i n squared A cos squared B minus s i n squared B c o s squared A over denominator c o s squared A c o s squared B end fraction end style end fraction space space space space space space space space space space space space equals fraction numerator begin display style open parentheses s i n squared A minus s i n squared B close parentheses c o s squared A end style over denominator begin display style s i n squared A c o s squared B minus s i n squared B c o s squared A end style end fraction space space space space space space space space space space space space equals fraction numerator begin display style open parentheses 1 minus cos squared A minus 1 plus cos squared B close parentheses c o s squared A end style over denominator begin display style open parentheses 1 minus c o s squared A close parentheses c o s squared B minus open parentheses 1 minus cos squared B close parentheses c o s squared A end style end fraction space space space space space space space space space space space space equals fraction numerator begin display style open parentheses cos squared B minus c o s squared A close parentheses c o s squared A end style over denominator begin display style open parentheses c o s squared B minus c o s squared B c o s squared A close parentheses minus open parentheses c o s squared A minus c o s squared A c o s squared B close parentheses end style end fraction space space space space space space space space space space space space equals fraction numerator begin display style open parentheses c o s squared B minus c o s squared A close parentheses c o s squared A end style over denominator begin display style open parentheses c o s squared B minus c o s squared A minus c o s squared B c o s squared A plus c o s squared B c o s squared A close parentheses end style end fraction space space space space space space space space space space space space equals fraction numerator begin display style open parentheses c o s squared B minus c o s squared A close parentheses c o s squared A end style over denominator begin display style open parentheses c o s squared B minus c o s squared A close parentheses end style end fraction space space space space space space space space space space space space equals c o s squared A

Answered by Vimala Ramamurthy | 8th Aug, 2015, 07:54: PM