We have to prove that (sin A + cos B)/(sin A - cos B) = (sec B + csc A)/(sec B - csc A)
We use the definitions: sec x = 1/cos x and csc x = 1/ sin x
(sin A + cos B)/(sin A - cos B)
=> (1/ csc A + 1/sec B)/ (1/csc A - 1/sec B)
making the denominator the same
=> [(sec B + csc A)/(csc A * sec B)]/[(sec B - csc A)/(csc A * sec B)]
canceling the common denominator
=> [(sec B + csc A)]/[(sec B - csc A)]
This proves that (sin A + cos B)/(sin A - cos B) = (sec B + csc A)/(sec B - csc A)
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