I feel so dumb because of these half angle trig identities!

FabZeros

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Jun 22, 2014
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Since I am learning by myself and I have no talent, it was inevitable that I would come to such a roadblock. I've completed every problem in the book except for these latest ones...

Please help me with them!!!! But also teach me how to think when verifying these identities! I feel like all my dreams of becoming successful at anything is quickly being deflated. If I can't even do high school math, how can I survive college?

well I've tried and failed to verify all 4 of these... Please teach me how to verify them! Thank you!
 

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Since I am learning by myself and I have no talent, it was inevitable that I would come to such a roadblock. I've completed every problem in the book except for these latest ones...

Please help me with them!!!! But also teach me how to think when verifying these identities! I feel like all my dreams of becoming successful at anything is quickly being deflated. If I can't even do high school math, how can I survive college?

well I've tried and failed to verify all 4 of these... Please teach me how to verify them! Thank you!
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There are no standard method to solve all these problems. You have to use your knowledge of algebra and trignometry to solve these problems.

64 sin(3x) + sin(x) = 4sinx-4sin3x

sin(3x)

= sin(2x + x)

= sin(2x)*cos(x) + sin(x)*cos(2x)

= [2sin(x)cos(x)]*cos(x) + sin(x)*[2cos2(x)-1]

= 2sin(x)cos2(x) + 2sin(x)cos2(x) - sin(x)

= 4sin(x)cos2(x) - sin(x)

= 4sin(x)*{1-sin2(x)] - sin(x)........ Now continue

Hint for 65 & 66 → use identities a3 ± b3 = (a ± b)*(a2 ± ab + b2) and cos2(Θ) + sin2(Θ) = 1

for 67 use substitution u = x/2 and use identity sec(u) = 1/cos(u)
 
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