Question

prove that cot A/2 + tan A/2 = 2cosecA​

Answer 1

tanA/2+ cotA/2=
sin(A/2)/cos(A/2)+ cos(A/2)/sin(A/2)=
[sin^2(A/2)+cos^2(A/2)]/sin(A/2)cos(A/2)=
1/[1/2sin2A/2]=2/sinA=2cosecA

1/(cosA+sinA)+1/(cosA-sinA)=
(cosA-sinA+cosA+sinA)/(cosA+sinA)(cosA-sinA)=
2cosA/[cos^2(A)-sin^2(A)]=
2cosA/cos2A=
2cosA*sin2A/cos2A*sin2A=
tan2A*2cosA/sin2A=
tan2A* 2cosA/2sinAcosA=
tan2A/sinA=
tan2A*1/sinA=
tan2A*cosecA