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Question
Prove that:
`(cos^2 "A")/(cos "A" - sin "A") + (sin "A")/(1 - cot "A")` = sin A + cos A
Solution
LHS = `(cos^2 "A")/(cos "A" - sin "A") + (sin "A")/(1 - cot "A")`
`= (cos^2 "A")/(cos "A" - sin "A") + (sin "A")/(1 - (cos "A")/(sin "A"))`
`= (cos^2 "A")/(cos "A" - sin "A") + (sin "A")/((sin "A" - cos "A")/(sin "A"))`
`= (cos^2 "A")/(cos "A" - sin "A") + (sin^2 "A")/ (sin "A" - cos "A")`
`= (cos^2 "A")/(cos "A" - sin "A") - (sin^2 "A")/(cos "A" - sin "A")`
`= (cos^2 "A" - sin^2 "A")/(cos "A" - sin "A")`
`= ((cos "A" + sin "A")(cos "A" - sin "A"))/((cos "A" - sin "A"))`
= sin A + cos A ...(RHS)
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