Homework Solution: Show the following trigonometric identity: tan 4x = 4 tan x – 4 tan^3 x/1 – 6 tan^2 x + tan^4 x steps: a) Create a…

    1) Show the following trigonometric identity: 4 tanx- 4 tan3x 1 - 6tan2x tan4x tan 4x = steps: a) Create an array of length 100, between [0, 2*pi b) Create two arrays for left hand side and right hand side of the identity c) Show the difference is zero (use sum, and abs function of matlab)
    Show the following trigonometric identity: tan 4x = 4 tan x - 4 tan^3 x/1 - 6 tan^2 x + tan^4 x steps: a) Create an array of length 100, between [0, 2*pi] b) Create two arrays for left hand side and right hand side of the identity c) Show the difference is zero (use sum, and abs function of matlab)

    Expert Answer

     
    main.m clc clear

    1) Show the aftercited trigonometric personality: 4 tanx- 4 tan3x 1 - 6tan2x tan4x tan 4x = steps: a) Create an rank of prolixity 100, betwixt [0, 2*pi b) Create couple ranks coercion left index party and just index party of the personality c) Show the dissimilitude is nothing (portraiture blend, and abs capacity of matlab)

    Show the aftercited trigonometric personality: tan 4x = 4 tan x – 4 tan^3 x/1 – 6 tan^2 x + tan^4 x steps: a) Create an rank of prolixity 100, betwixt [0, 2*pi] b) Create couple ranks coercion left index party and just index party of the personality c) Show the dissimilitude is nothing (portraiture blend, and abs capacity of matlab)

    Expert Confutation

     

    main.m

    clc
    clear
    x = linspace(0,2*pi)
    array1 = tan(4*x)
    array2 = ((4*tan(x))-(4*(tan(x)).^3))./(1-(6*(tan(x)).^2)+(tan(x)).^4)
    sum1=sum(abs(array1))
    sum2=sum(abs(array2))
    dissimilitude = foundation(sum1-sum2)

    Output :-

    x =

    Columns 1 through 16

    0    0.0635    0.1269    0.1904    0.2539    0.3173    0.3808    0.4443    0.5077    0.5712    0.6347    0.6981    0.7616    0.8251    0.8885    0.9520

    Columns 17 through 32

    1.0155    1.0789    1.1424    1.2059    1.2693    1.3328    1.3963    1.4597    1.5232    1.5867    1.6501    1.7136    1.7771    1.8405    1.9040    1.9675

    Columns 33 through 48

    2.0309    2.0944    2.1579    2.2213    2.2848    2.3483    2.4117    2.4752    2.5387    2.6021    2.6656    2.7291    2.7925    2.8560    2.9195    2.9829

    Columns 49 through 64

    3.0464    3.1099    3.1733    3.2368    3.3003    3.3637    3.4272    3.4907    3.5541    3.6176    3.6811    3.7445    3.8080    3.8715    3.9349    3.9984

    Columns 65 through 80

    4.0619    4.1253    4.1888    4.2523    4.3157    4.3792    4.4427    4.5061    4.5696    4.6331    4.6965    4.7600    4.8235    4.8869    4.9504    5.0139

    Columns 81 through 96

    5.0773    5.1408    5.2043    5.2677    5.3312    5.3947    5.4581    5.5216    5.5851    5.6485    5.7120    5.7755    5.8389    5.9024    5.9659    6.0293

    Columns 97 through 100

    6.0928    6.1563    6.2197    6.2832

    array1 =

    Columns 1 through 16

    0    0.2595    0.5564    0.9535    1.6117    3.2160   20.9926   -4.7792   -2.0177   -1.1541   -0.6884   -0.3640   -0.0955    0.1600    0.4376    0.7864

    Columns 17 through 32

    1.3140    2.3874    6.9552   -8.9666   -2.6175   -1.4043   -0.8391   -0.4760   -0.1927    0.0636    0.3284    0.6427    1.0827    1.8664    4.1221 -63.0201

    Columns 33 through 48

    -3.6170   -1.7321   -1.0160   -0.5987   -0.2936   -0.0317    0.2259    0.5155    0.8947    1.5031    2.8893   12.5786   -5.6713   -2.1897   -1.2309   -0.7363

    Columns 49 through 64

    -0.4003   -0.1276    0.1276    0.4003    0.7363    1.2309    2.1897    5.6713 -12.5786   -2.8893   -1.5031   -0.8947   -0.5155   -0.2259    0.0317    0.2936

    Columns 65 through 80

    0.5987    1.0160    1.7321    3.6170   63.0201   -4.1221   -1.8664   -1.0827   -0.6427   -0.3284   -0.0636    0.1927    0.4760    0.8391    1.4043    2.6175

    Columns 81 through 96

    8.9666   -6.9552   -2.3874   -1.3140   -0.7864   -0.4376   -0.1600    0.0955    0.3640    0.6884    1.1541    2.0177    4.7792 -20.9926   -3.2160   -1.6117

    Columns 97 through 100

    -0.9535   -0.5564   -0.2595   -0.0000

    array2 =

    Columns 1 through 16

    0    0.2595    0.5564    0.9535    1.6117    3.2160   20.9926   -4.7792   -2.0177   -1.1541   -0.6884   -0.3640   -0.0955    0.1600    0.4376    0.7864

    Columns 17 through 32

    1.3140    2.3874    6.9552   -8.9666   -2.6175   -1.4043   -0.8391   -0.4760   -0.1927    0.0636    0.3284    0.6427    1.0827    1.8664    4.1221 -63.0201

    Columns 33 through 48

    -3.6170   -1.7321   -1.0160   -0.5987   -0.2936   -0.0317    0.2259    0.5155    0.8947    1.5031    2.8893   12.5786   -5.6713   -2.1897   -1.2309   -0.7363

    Columns 49 through 64

    -0.4003   -0.1276    0.1276    0.4003    0.7363    1.2309    2.1897    5.6713 -12.5786   -2.8893   -1.5031   -0.8947   -0.5155   -0.2259    0.0317    0.2936

    Columns 65 through 80

    0.5987    1.0160    1.7321    3.6170   63.0201   -4.1221   -1.8664   -1.0827   -0.6427   -0.3284   -0.0636    0.1927    0.4760    0.8391    1.4043    2.6175

    Columns 81 through 96

    8.9666   -6.9552   -2.3874   -1.3140   -0.7864   -0.4376   -0.1600    0.0955    0.3640    0.6884    1.1541    2.0177    4.7792 -20.9926   -3.2160   -1.6117

    Columns 97 through 100

    -0.9535   -0.5564   -0.2595   -0.0000

    sum1 =

    341.2068

    sum2 =

    341.2068

    dissimilitude =

    0