1.P r o v e space t h e space I d e n t i t y colon fraction numerator c o t A minus cos A over denominator c o t A plus cos A end fraction equals fraction numerator cos e c A minus 1 over denominator cos e c A plus 1 end fraction
 

Asked by Ra. | 18th Sep, 2015, 09:54: PM

Expert Answer:

C o n s i d e r space t h e space l e f t space h a n d space s i d e space o f space t h e space e x p r e s s i o n colon T h u s comma fraction numerator c o t A minus cos A over denominator c o t A plus cos A end fraction equals fraction numerator begin display style fraction numerator cos A over denominator sin A end fraction end style minus cos A over denominator fraction numerator c o s A over denominator s i n A end fraction plus c o s A end fraction 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 begin display style fraction numerator c o s A minus cos A sin A over denominator s i n A end fraction end style over denominator fraction numerator c o s A plus c o s A s i n A over denominator s i n A end fraction end fraction 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 begin display style fraction numerator c o s A open parentheses 1 minus s i n A close parentheses over denominator s i n A end fraction end style over denominator fraction numerator c o s A open parentheses 1 plus s i n A close parentheses over denominator s i n A end fraction end fraction 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 begin display style fraction numerator begin display style open parentheses 1 minus sin A close parentheses end style over denominator sin A end fraction end style over denominator fraction numerator begin display style open parentheses 1 plus s i n A close parentheses end style over denominator s i n A end fraction end fraction 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 begin display style open parentheses fraction numerator 1 over denominator sin A end fraction minus 1 close parentheses end style over denominator open parentheses fraction numerator 1 over denominator s i n A end fraction plus 1 close parentheses end fraction 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 begin display style open parentheses cos e c A minus 1 close parentheses end style over denominator open parentheses c o s e c A plus 1 close parentheses end fraction H e n c e space p r o v e d.

Answered by Vimala Ramamurthy | 19th Sep, 2015, 09:41: AM