tan(1.9*c)*tan(1.9)+cot(- ... n(pi)^(2)/2-cos(pi)^(2)/2 (уравнение)

Найду корень уравнения: tan(1.9*c)*tan(1.9)+cot(-5*pi/6)^(2)=-sin(pi)^(2)/2-cos(pi)^(2)/2

Вы ввели

                                      2           2    
   /19*c\    /19\      2/-5*pi\   -sin (pi)    cos (pi)
tan|----|*tan|--| + cot |-----| = ---------- - --------
   \ 10 /    \10/       \  6  /       2           2    

$$\tan{\left(\frac{19}{10} \right)} \tan{\left(\frac{19 c}{10} \right)} + \cot^{2}{\left(- \frac{5 \pi}{6} \right)} = - \frac{\cos^{2}{\left(\pi \right)}}{2} + \frac{\left(-1\right) \sin^{2}{\left(\pi \right)}}{2}$$

Подробное решение

Дано уравнение
$$\tan{\left(\frac{19}{10} \right)} \tan{\left(\frac{19 c}{10} \right)} + \cot^{2}{\left(- \frac{5 \pi}{6} \right)} = - \frac{\cos^{2}{\left(\pi \right)}}{2} + \frac{\left(-1\right) \sin^{2}{\left(\pi \right)}}{2}$$
- это простейшее тригонометрическое ур-ние

Разделим обе части ур-ния на tan(19/10)

Ур-ние превратится в
$$\tan{\left(\frac{19 c}{10} \right)} = - \frac{7}{2 \tan{\left(\frac{19}{10} \right)}}$$
Это ур-ние преобразуется в
$$\frac{19 c}{10} = \pi n + \operatorname{atan}{\left(- \frac{7}{2 \tan{\left(\frac{19}{10} \right)}} \right)}$$
Или
$$\frac{19 c}{10} = \pi n - \operatorname{atan}{\left(\frac{7}{2 \tan{\left(\frac{19}{10} \right)}} \right)}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$\frac{19}{10}$$
получим ответ:
$$c_{1} = \frac{10 \pi n}{19} - \frac{10 \operatorname{atan}{\left(\frac{7}{2 \tan{\left(\frac{19}{10} \right)}} \right)}}{19}$$

Быстрый ответ

             /    7    \
     -10*atan|---------|
             |     /19\|
             |2*tan|--||
             \     \10//
c1 = -------------------
              19        

$$c_{1} = - \frac{10 \operatorname{atan}{\left(\frac{7}{2 \tan{\left(\frac{19}{10} \right)}} \right)}}{19}$$

Сумма и произведение корней

сумма

           /    7    \
    10*atan|---------|
           |     /19\|
           |2*tan|--||
           \     \10//
0 - ------------------
            19        

$$0 - \frac{10 \operatorname{atan}{\left(\frac{7}{2 \tan{\left(\frac{19}{10} \right)}} \right)}}{19}$$

=

        /    7    \
-10*atan|---------|
        |     /19\|
        |2*tan|--||
        \     \10//
-------------------
         19        

$$- \frac{10 \operatorname{atan}{\left(\frac{7}{2 \tan{\left(\frac{19}{10} \right)}} \right)}}{19}$$

произведение

          /    7    \
  -10*atan|---------|
          |     /19\|
          |2*tan|--||
          \     \10//
1*-------------------
           19        

$$1 \left(- \frac{10 \operatorname{atan}{\left(\frac{7}{2 \tan{\left(\frac{19}{10} \right)}} \right)}}{19}\right)$$

=

        /    7    \
-10*atan|---------|
        |     /19\|
        |2*tan|--||
        \     \10//
-------------------
         19        

$$- \frac{10 \operatorname{atan}{\left(\frac{7}{2 \tan{\left(\frac{19}{10} \right)}} \right)}}{19}$$

Численный ответ

c1 = 69.9058911819971

c2 = 91.400998811822

c3 = -97.0945604035656

c4 = 2.11362865716471

c5 = -7.80719024890832

c6 = 26.9156759223473

c7 = -83.8668018621349

c8 = -67.3321036853465

c9 = -44.1835262378428

c10 = 40.143434463778

c11 = 56.6781326405664

c12 = -6.15372043122948

c13 = 36.8364948284203

c14 = 58.3316024582452

c15 = 64.9454817289606

c16 = -78.9063924090984

c17 = -2.84678079587181

c18 = 74.8663006350336

c19 = -98.7480302212444

c20 = -64.0251640499888

c21 = -29.3022978787332

c22 = 86.4405893587855

c23 = 79.8267100880701

c24 = 41.7969042814568

c25 = -47.4904658732004

c26 = 38.4899646460992

c27 = -54.1043451439158

c28 = -37.5696469671274

c29 = -60.7182244146312

c30 = 98.0148780825373

c31 = -82.2133320444561

c32 = 101.321817717895

c33 = 7.07403811020122

c34 = 31.8760853753838

c35 = 96.3614082648585

c36 = -70.6390433207042

c37 = -55.7578149615946

c38 = -1.19331097819297

c39 = -9.46066006658716

c40 = 94.7079384471797

c41 = -85.5202716798137

c42 = -19.3814789726602

c43 = 63.2920119112817

c44 = -59.0647545969523

c45 = -25.9953582433755

c46 = -95.4410905858868

c47 = -16.0745393373025

c48 = 50.064253369851

c49 = 15.3413871985954

c50 = -68.9855735030253

c51 = 83.1336497234278

c52 = 48.4107835521722

c53 = -50.7974055085581

c54 = 59.9850722759241

c55 = 55.0246628228875

c56 = 66.5989515466394

c57 = -30.9557676964121

c58 = -35.9161771494486

c59 = 10.3809777455589

c60 = 8.72750792788006

c61 = 73.2128308173548

c62 = -32.6092375140909

c63 = -11.114129884266

c64 = 76.5197704527124

c65 = 21.9552664693108

c66 = -57.4112847792735

c67 = 53.3711930052087

c68 = -75.5994527737407

c69 = 20.3017966516319

c70 = -21.034948790339

c71 = 18.6483268339531

c72 = 0.460158839485869

c73 = -49.1439356908793

c74 = -93.7876207682079

c75 = 25.2622061046684

c76 = -40.8765866024851

c77 = 93.0544686295008

c78 = 45.1038439168145

c79 = -65.6786338676677

c80 = 12.0344475632377

c81 = 28.5691457400261

c82 = 30.222615557705

c83 = -77.2529225914195

c84 = 88.0940591764643

c85 = 5.42056829252238

c86 = 35.1830250107415

c87 = -45.8369960555216

c88 = 16.9948570162743

c89 = -87.1737414974926

c90 = 46.7573137344934

c91 = -17.7280091549814

c92 = 68.2524213643183

c93 = -12.7675997019448

c94 = -39.2231167848063

c95 = 84.7871195411066

c96 = -73.9459829560619

c97 = -92.1341509505291

c98 = -27.6488280610544

c99 = 78.1732402703913

c100 = -22.6884186080179

c101 = -88.8272113151714

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