HELP!! Trig internal tomorrow and I'm still having ridiculous trouible proving things!!! Please help?

I'm currently doing some practice questions and came across one that looked simple at first until i tried it, then became hideously lost in a tangle of sins and cos's.

here's the question.

Prove that (sin2A - sinA) / (cos2A - cosA + 1) = tanA

ferozeso2009-04-07T03:15:44Z

Favorite Answer

Start with the more complicated side.

LHS
= (sin2A - sinA) / (cos2A - cosA + 1)
= (2sinAcosA - sinA) / (2cos^2 A - 1 - cosA + 1) ------- [*]
= sinA(2cosA - 1) / cosA(2cosA - 1)
= sinA / cos A
= tanA
= RHS.

[*] ------- cos2A = 2cos^2 A - 1 is chosen over the others because it will cancel off the +1 and when cosA is factored later, the fraction can be further simplified... Practice makes perfect.

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