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Question
Prove the following identity :
`cosA/(1 - tanA) + sin^2A/(sinA - cosA) = cosA + sinA`
Solution
LHS = `cosA/(1 - tanA) + sin^2A/(sinA - cosA)`
= `cosA/(1 - sinA/cosA) + sin^2A/(sinA - cosA)`
= `cosA/((cosA - sinA)/(cosA)) + sin^2A/(sinA - cosA)`
= `cos^2A/((cosA - sinA)) - sin^2A/((cosA - sinA))`
= `(cos^2A - sin^2A)/(cosA - sinA) = ((cosA + sinA)(cosA - sinA))/((cosA - sinA))`
= (cosA + sinA)
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