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Calculus/solve the proof

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Expert: Alon Mandes - 5/20/2009


Question
cos3x = 4cos^3x-3cosx

Answer
The basic rules we will use in this proof will be :
1. sin2x=2sinxcosx
2. sin²x+cos²x=1 -> sin²x=1-cos²x
3. cosx=½[1+cos2x] -> cos2x=2cos²x-1
4. cos(α+β)=cosαcosβ-sinαsinβ
Lets get to work:
cos3x=cos(x+2x)=cosxcos2x-sinxsin2x=cosx[2cos²x-1]-sinx[2sinxcosx]=
=2cos³x-cosx-2sin²xcosx=2cos³x-cosx-2(1-cos²x)cosx=
2cos³x-cosx-2cosx+2cos³x=4cos³x-3cosx . Q.E.D

Alon.

Calculus

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Alon Mandes

Expertise

Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .

Experience

1. I'm a team member of mathnerds (math site for answering questions) 2. I'm a team member in the Student's Union of the Technion, helping students who have problems in mathematics. 3. 2 years of experience as a math teacher in college. 4. I give free homework help for high school students in Mathematics & Physics. 5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" , "Complex Functions".

Organizations
Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.

Education/Credentials
M.A in Mathematics & Bs.c in Electronics.

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