Solving Trigonometric Identity EXAMPLE | Pre-Calculus

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In this example we solve a common pre-calculus questions involving trigonometric identities.
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In the 3rd row step how is the 2cosx+2 taken back down to 2(cosx+1)? I assume the 1 is added due to the identity, why is it removed after?

nikosoup
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Why do the numerators double in the first step

habibtimadeline
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How did you make the common denominator ?

FunkyMonkey
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But can you use mathematical induction there, as well?

miggythenerd
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Factorization will be the death of me 😅❤

Netchi-yqpb
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Yall can still turn to Jesus God bless

caleb.
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