CBSE Class 10 Answered

if cosecA+cotA=P then, find the value of secA-tanA. {hint: ans. is 1/p}

Asked by shubham8308244792 | 12 Sep, 2015, 12:22: PM

Expert Answer

$g i v e n space t h a t space cos e c A plus c o t A equals P rightwards double arrow fraction numerator 1 over denominator sin A end fraction plus fraction numerator cos A over denominator sin A end fraction equals P rightwards double arrow fraction numerator 1 plus cos A over denominator sin A end fraction equals P rightwards double arrow fraction numerator 2 c o s squared A over 2 over denominator 2 s i n begin display style A over 2 end style cos A over 2 end fraction equals P space space space space space space open square brackets because 1 plus cos 2 theta equals 2 cos squared theta space a n d space sin 2 theta equals 2 sin theta cos theta close square brackets rightwards double arrow fraction numerator c o s A over 2 over denominator s i n begin display style A over 2 end style end fraction equals P rightwards double arrow c o t A over 2 equals P rightwards double arrow tan A over 2 equals 1 over P C o n s i d e r space s e c A minus tan A equals fraction numerator 1 over denominator cos A end fraction minus fraction numerator sin A over denominator cos A end fraction space space space space space space space space space space space space space space space space space space space equals fraction numerator 1 minus s i n A over denominator 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 equals fraction numerator c o s squared A over 2 plus sin squared A over 2 minus 2 s i n A over 2 c o s A over 2 over denominator c o s squared A over 2 minus s i n squared A over 2 end fraction space space space space space space space space space space space space space space space space space space space equals fraction numerator open parentheses cos A over 2 minus sin A over 2 close parentheses squared over denominator open parentheses cos A over 2 minus sin A over 2 close parentheses open parentheses c o s A over 2 plus s i n A over 2 close parentheses end fraction space space space space space space space space space space space space space space space space space space space equals fraction numerator open parentheses c o s A over 2 minus s i n A over 2 close parentheses over denominator open parentheses c o s A over 2 plus s i n A over 2 close parentheses end fraction space space space space space space space space space space space space space space space space space space space equals fraction numerator c o s A over 2 open parentheses 1 minus begin display style fraction numerator sin A over 2 over denominator c o s A over 2 end fraction end style close parentheses over denominator c o s A over 2 open parentheses 1 plus fraction numerator s i n A over 2 over denominator c o s A over 2 end fraction close parentheses end fraction space space space space space space space space space space space space space space space space space space space equals fraction numerator c o s A over 2 open parentheses 1 minus t a n A over 2 close parentheses over denominator c o s A over 2 open parentheses 1 plus t a n A over 2 close parentheses end fraction space space space space space space space space space space space space space space space space space space space equals fraction numerator open parentheses 1 minus 1 over P close parentheses over denominator open parentheses 1 plus 1 over P close parentheses end fraction space space space space space space space space space space space space space space space space space space space equals fraction numerator open parentheses fraction numerator P minus 1 over denominator P end fraction close parentheses over denominator open parentheses fraction numerator P plus 1 over denominator P end fraction close parentheses end fraction space space space space space space space space space space space space space space space space space space space equals fraction numerator open parentheses P minus 1 close parentheses over denominator open parentheses P 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$