prove that sin A(1+tan A)+cos A(1+cot A)= sec A+ cosec A

Answer 1

multiply the left side by sinAcosA/(sinAcosA)

sin^2A*(cosA+sinA)+cos^2A*(sin+cosA)/ ( )

(cosA+sinA)(sin^2+ cos^2)/ ( )

1/sinA + 1/Cos A

cscA + secA

qed