prove the following identity :-
plz...... hlp me in this question I'll mark you as a
Answers
Proof:
sinA/(secA+tanA-1)+cosA/(cosecA+cotA-1) = 1
=> sinA(cosecA+cotA-1) + cosA(secA+tanA-1)/ (secA+tanA-1)(cosecA+cotA-1) = 1
=>sinAcosecA+sinAcotA- sinA + cosAsecA+cosAtanA-cosA/(secAcosecA+secAcotA-secA+tanAcosecA+tanAcotA-tanA-cosecA-cotA +1)=1
=>sinA.(1/sinA)+sinAcotA-sinA+cosA.(1/cosA)+cosAtanA-cosA/ (secAcosecA+ secAcotA-secA+tanAcosecA+tanA.(1/tanA)-tanA-cosecA-cotA+1)=1
=>1+sinAcotA-sinA+1+cosAtanA-cosA/(secAcosecA+secAcotA-secA+tanAcosecA+1-tanA-cosecA-cotA+1)= 1
=>1+sinA(1/tanA)-sinA+1+cosAtanA-cosA/(1/cosA)(1/sinA)+(1/cosA)(1/tanA)-(1/cosA)+tanA(1/sinA)+1-tanA-(1/sinA)-(1/tanA)+1= 1
=>1+sinA(cosA/sinA)-sinA+ cosA(sinA/cosA)-cosA/(1/sinAcosA)+(1/cosA.sinA/cosA)-(1/cosA)+ sinA/cosA(1/sinA)+1-(sinA/cosA)-(1/sinA)-(cosA/sinA)+1=1
=>1+cosA-sinA+sinA-cosA/(1/sinAcosA)+(1/sinA)-(1/cosA)+(1/cosA)+1-(sinAcosA)-(1/sinA)-(cosA/sinA)+1=1
=>1/(1/sinAcosA)+[(cosA-sinA)/(sinAcosA)]+(1/cosA)+1-{(sin²AcosA-1)/sinA}-(cosA/sinA)+1=1
=>1/(1/sinAcosA)+[(cosA-sinA)/(sinAcosA)]+secA+1-[(sin²AcosA-1)/sinA]-cotA+1=1
=>1/(cosecAsecA)+[(cosA-sinA)/(sinAcosA)]+ secA +1- [(sin²AcosA-1)/sinA]-cotA+1=1
=>1/-1+1+1= 1
=>1/1= 1
:)