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Calculus/Help on Proof

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Expert: Alon Mandes - 11/14/2008


Question
I cam across this problem in one of my math magazines, and I've been on it for days but can't seem to figure it out. It goes like this.

Prove that this equation is an identity:
((1+sinx+cosX)/(1+sinx-cosx)) = ((1+cosx)/(sinx))

I have no idea what to do.

Answer
Ok Liz, let's start from the very well know identity :
(1+cosx)(1-cosx)=(sinx)^2. (I will leave it for you to confirm it).
So, let's find out what will happen when we plug sinx in the 2nd
bracket : (1+cosx)(1-cosx+sinx)=?
(1+cosx)(1-cos+sinx)=(1+cosx)(1-cosx)+(1+cosx)sinx=
(sinx)^2+sinx+sinxcosx=sinx[sinx+1+cosx], so :
(1+cosx)(1-cosx+sinx)=sinx[sinx+1+cosx] , & that means :
(1-cosx+sinx)           1+cosx
----------------  =  ----------------
[sinx+1+cosx]            sinx

Q.E.D

Alon.

Calculus

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Alon Mandes

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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 .

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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".

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

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

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