double compound formulae and other bits: If θ is fixed real number w/ 0≤θ<2π, show...

[sharp.NOT]

double compound formulae and other bits: If θ is fixed real number w/ 0≤θ<2π, show...

Hi, could anyone please help me with following questions:

1) If θ is a fixed real number with 0≤θ<2π Show that forall real x, cos(x)+cos(x+θ)=Acos(x+φ) where φ=θ/2 and A=2cos(θ/2)
2) Determine θ if A=1/4 and if A=-1
any help appreciated, thank you.

 

[Deleted member 4993]

Hi, could anyone please help me with following questions:

1) If θ is a fixed real number with 0≤θ<2π Show that forall real x, cos(x)+cos(x+θ)=Acos(x+φ) where φ=θ/2 and A=2cos(θ/2)
2) Determine θ if A=1/4 and if A=-1
any help appreciated, thank you.

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[stapel]

Hi, could anyone please help me with following questions:

1) If θ is a fixed real number with 0≤θ<2π Show that forall real x, cos(x)+cos(x+θ)=Acos(x+φ) where φ=θ/2 and A=2cos(θ/2)
2) Determine θ if A=1/4 and if A=-1

We'll be glad to help! But first, we'll need to know where you're stuck. For instance, what identities have they given you? How have you applied identities to the equation? And so forth?

Please be complete. Thank you!