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Question
good morning .
can you help me please in solving the following equation :
sin (2x ) + tan ( x ) = 2
note: i know by attempting that the ans. is x= 45 degree.
Let's use the trigonometrical identity : sin(2x)=tan(x)/[1+tan^2(x)]
We get : tan(x)/[1+tan^2(x)]+tan(x)=2. Let's set tan(x)=λ. Then we
get : λ+λ/(1+λ^2)=2 --> λ^3-2λ^2+3λ-2=0 This can also be written as
(λ^2-2λ+2)(λ-1)=0. Which means λ=1. --> tang(x)=1 --> x=π/4.
Alon.
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Answers by Expert:
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".
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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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