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(sinA)/(1-cosA)-(1-cosA)/(sinA)=...

`(sinA)/(1-cosA)-(1-cosA)/(sinA)=`

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cosA/(1−sinA) =

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

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: 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.

Show that (1+sinA)/(cosA)+(cosB)/(1-sinB)=(2sinA-2sinB)/(sin(A-B)+cosA-cosB)

Show that (1+sinA)/(cosA)+(cosB)/(1-sinB)=(2sinA-2sinB)/(sin(A-B)+cosA-cosB)

Show that (1+sinA)/(cosA)+(cosB)/(1-sinB)=(2sinA-2sinB)/(sin(A-B)+cosA-cosB)

The simplified value of 1- (sin^(2)A)/(1+ cosA) + (1+ cosA)/(sinA) - (sinA)/(1- cosA) is:

Prove the following identities: (sinA+cosA)/(sinA-cosA)+(sinA-cosA)/(sinA+cosA)=2/(sin^2A-cos^2A)=2/(2sin^2A-1)=2/(1-2cos^2A)