SOLUTION: Proving identities. How do I prove that: i) tanē(x) - sinē(x) = tanē(x) sinē(x) ii) (1+ cos(x) + cos(2x))/ (sin(x) + sin(2x)) = cot (x) I tried question 1 and i got stuck at

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Question 1106380: Proving identities.
How do I prove that:
i) tanē(x) - sinē(x) = tanē(x) sinē(x)
ii) (1+ cos(x) + cos(2x))/ (sin(x) + sin(2x)) = cot (x)
I tried question 1 and i got stuck at sin2x - cos2x - cos4x which seemed quite wrong to me. Thanks :)
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
i) tanē(x) - sinē(x) = tanē(x) sinē(x) 

change tanē(x) to sinē(x)/cosē(x)



Get LCD of cosē(x)



Factor out sinē(x) on top:



Replace 1-cosē(x) by sinē(x)



Break into a product:



Replace  by 



Turn backward



-----------------------------

ii) 

Use identities for cos(2x) and sin(2x)





Factor out common factors on top and bottom:









Edwin
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