SOLUTION: Prove the identity (sin A - cos A)/(sin A) + (cos A - sin A)/(cos A) = 2 - sec A csc A

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Question 1104648: Prove the identity
(sin A - cos A)/(sin A) + (cos A - sin A)/(cos A) = 2 - sec A csc A
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Prove the identity
(sin A - cos A)/(sin A) + (cos A - sin A)/(cos A) = 2 - sec A csc A
(1 - cot) + (1 - tan) = 2 - 1/(sin*cos)
2 - tan - cot = 2 - 1/(sin*cos)
tan + cot = 1/(sin*cos)
Multiply thru by sin*cos
sin^2 + cos^2 = 1
I'm convinced.