Prove that `tan(A/2)=sqrt((1-cosA)/(1+cosA))`

Prove that: i) sqrt((1-cosA)/(1+cosA))="cosec"A-cotA ii) sqrt((1+sinA)/(1-sinA))=secA-tanA

Prove that : sqrt((1+cosA)/(1-cosA))+sqrt((1-cosA)/(1+cosA))=2" cosec"A

Prove that: i) tan(45^(@)-A/2) = (1-sinA)/(cosA) ii) tan(45^(@)+A/2)= (cosA)/(1-sinA)

Prove that: sqrt((1+cosA)/(1-cosA))={:("cosec"A+cotA, if 0ltAltpi),(-"cosec"A-cotA, if pi lt A lt 2pi):}

cosA/(1−sinA) =

Prove that : (i) (1)/(1-cosA)+(1)/(1+cosA)=2"cosec"^(2)A " " (ii) (1)/(1-sinA)-(1)/(1+sinA)=2secAtanA

If sin A=(3)/(5) , prove that tanA+(1)/(cosA)=2 or -2

Prove that (1+sin2A)/(cos2A)=(cosA+sinA)/(cosA-sinA)=tan((pi)/(4)+A)

Prove that: cotA/2-tanA/2=(cosA/2)/(sinA/2)-(sinA/2)/(cosA/2) =(cos^(2)A/2-sin^(2)A/2)/(sinA/2cosA/2) =cosA/(1/2.(2sinA/2cosA/2)) =(2cosA)/(sinA)=2cotA = RHS. Hence Proved.

Prove that : (secA+tanA)(1-sinA)=cosA