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

[FabZeros]

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!

 

[Deleted member 4993]

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!

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)