If sinA+cosA=p and secA+cosecA=q,then the value of q(p^3-1)/p.

Asked by nitinkumarsingh.singh.75 | 20th Nov, 2015, 07:16: PM

Expert Answer:

G i v e n space t h a t space sin A plus cos A equals p... left parenthesis 1 right parenthesis a n d s e c A plus cos e c A equals q... left parenthesis 2 right parenthesis S q u a r i n g space e q u a t i o n space left parenthesis 1 right parenthesis comma space w e space h a v e comma open parentheses s i n A plus c o s A close parentheses squared equals p squared rightwards double arrow s i n squared A plus c o s squared A plus 2 s i n A c o s A equals p squared... left parenthesis 3 right parenthesis rightwards double arrow 1 plus 2 s i n A c o s A equals p squared rightwards double arrow 2 s i n A c o s A equals p squared minus 1... left parenthesis 4 right parenthesis rightwards double arrow s i n A c o s A equals fraction numerator p squared minus 1 over denominator 2 end fraction... left parenthesis 5 right parenthesis  S q u a r i n g space e q u a t i o n space left parenthesis 2 right parenthesis comma space w e space h a v e comma open parentheses s e c A plus c o s e c A close parentheses squared equals q squared rightwards double arrow open parentheses fraction numerator 1 over denominator c o s A end fraction plus fraction numerator 1 over denominator s i n A end fraction close parentheses squared equals q squared rightwards double arrow open square brackets fraction numerator c o s A plus s i n A over denominator c o s A s i n A end fraction close square brackets squared equals q squared rightwards double arrow s i n squared A plus c o s squared A plus 2 s i n A c o s A equals q squared c o s squared A s i n squared A... left parenthesis 6 right parenthesis F r o m space e q u a t i o n s space left parenthesis 3 right parenthesis comma space left parenthesis 5 right parenthesis space a n d space left parenthesis 6 right parenthesis comma space rightwards double arrow p squared equals q squared c o s squared A s i n squared A space rightwards double arrow p squared equals q squared s i n A c o s A space rightwards double arrow p equals q fraction numerator p squared minus 1 over denominator 2 end fraction rightwards double arrow 2 p equals q open parentheses p squared minus 1 close parentheses rightwards double arrow fraction numerator q open parentheses p squared minus 1 close parentheses over denominator p end fraction equals 2

Answered by Vimala Ramamurthy | 21st Nov, 2015, 07:09: PM