Prove that: sinA+cosB/sinA-cosB=secB+cscA/secB-cscA

Supposing that we have to prove that
(sinA+cosB)/(sinA-cosB) = (secB+cscA)/(secB-cscA), we'll cross multiply and we'll
get:

(sinA+cosB)(secB-cscA) =
(sinA-cosB)(secB+cscA)

We'll pu sec B = 1/cos B and  sec B
= 1/cos B

csc A = 1/sin A and sec A = 1/cos
A

We'll substitute secA,secB,cscA and cscB inside
brackets:

(sinA+cosB)(1/cos B - 1/sin A) =
(sinA-cosB)(1/cos B + 1/sin A)

We'll remove brackets using
FOIL method:

sinA/cosB - sinA/sinA + cosB/cosB - cosB/sinA
= sinA/cosB + sinA/sinA - cosB/cosB - cosB/sinA

sinA/cosB
-1 + 1- cosB/sinA = sinA/cosB + 1- 1 - cosB/sinA

We'll
eliminate like terms and we'll get LHS =
RHS:

sinA/cosB - cosB/sinA = sinA/cosB -
cosB/sinA