Дано

$$sin^{2}{left (x right )} + frac{3}{2} sin{left (2 x right )} = -1$$
Ответ

/ _______________________________________________________________________
| / _________ _________ | / / _________
| / 3/4 / -1 /atan(3) 3/4 / -1 /atan(3) | | | / -1 ________||
| _______________________________________________________________________ / 10 * / ——- *sin|——-| I*10 * / ——- *cos|——-| | |im| / ——- */ -3 – I ||
| / 4 ____ ________ /atan(1/3) 4 ____ ________ /atan(1/3) / / 1 + 3*I 2 / / 1 + 3*I 2 / | | / 1 + 3*I /|
x1 = pi – I*log| / / 10 */ -3 – I *sin|———| + I*/ 10 */ -3 – I *cos|———| * / ——————————– – ———————————- | + atan|—————————-|
/ 2 / 2 / / 10 10 / | / _________ |
| | / -1 ________||
|re| / ——- */ -3 – I ||
/ 1 + 3*I //

$$x_{1} = {atan}{left (frac{Im{left(sqrt{- frac{1}{1 + 3 i}} sqrt{-3 – i}right)}}{Re{left(sqrt{- frac{1}{1 + 3 i}} sqrt{-3 – i}right)}} right )} + pi – i log{left (sqrt{sqrt[4]{10} sqrt{-3 – i} sin{left (frac{1}{2} {atan}{left (frac{1}{3} right )} right )} + sqrt[4]{10} i sqrt{-3 – i} cos{left (frac{1}{2} {atan}{left (frac{1}{3} right )} right )}} sqrt{- frac{10^{frac{3}{4}} i}{10} sqrt{- frac{1}{1 + 3 i}} cos{left (frac{1}{2} {atan}{left (3 right )} right )} + frac{10^{frac{3}{4}}}{10} sqrt{- frac{1}{1 + 3 i}} sin{left (frac{1}{2} {atan}{left (3 right )} right )}} right )}$$

/ _______________________________________________________________________
| / _________ _________ | / / _________
| / 3/4 / -1 /atan(3) 3/4 / -1 /atan(3) | | | / -1 ________||
| _______________________________________________________________________ / 10 * / ——- *sin|——-| I*10 * / ——- *cos|——-| | |im| / ——- */ -3 – I ||
| / 4 ____ ________ /atan(1/3) 4 ____ ________ /atan(1/3) / / 1 + 3*I 2 / / 1 + 3*I 2 / | | / 1 + 3*I /|
x2 = – I*log| / / 10 */ -3 – I *sin|———| + I*/ 10 */ -3 – I *cos|———| * / ——————————– – ———————————- | + atan|—————————-|
/ 2 / 2 / / 10 10 / | / _________ |
| | / -1 ________||
|re| / ——- */ -3 – I ||
/ 1 + 3*I //

$$x_{2} = {atan}{left (frac{Im{left(sqrt{- frac{1}{1 + 3 i}} sqrt{-3 – i}right)}}{Re{left(sqrt{- frac{1}{1 + 3 i}} sqrt{-3 – i}right)}} right )} – i log{left (sqrt{sqrt[4]{10} sqrt{-3 – i} sin{left (frac{1}{2} {atan}{left (frac{1}{3} right )} right )} + sqrt[4]{10} i sqrt{-3 – i} cos{left (frac{1}{2} {atan}{left (frac{1}{3} right )} right )}} sqrt{- frac{10^{frac{3}{4}} i}{10} sqrt{- frac{1}{1 + 3 i}} cos{left (frac{1}{2} {atan}{left (3 right )} right )} + frac{10^{frac{3}{4}}}{10} sqrt{- frac{1}{1 + 3 i}} sin{left (frac{1}{2} {atan}{left (3 right )} right )}} right )}$$
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/ _______________________________________________________________________
| / _________ _________ | / / _________
| / 3/4 / -1 /atan(3) 3/4 / -1 /atan(3) | | | / -1 ________||
| _______________________________________________________________________ / 10 * / ——- *sin|——-| I*10 * / ——- *cos|——-| | |im| / ——- */ -3 + I ||
| / 4 ____ ________ /atan(1/3) 4 ____ ________ /atan(1/3) / / 1 + 3*I 2 / / 1 + 3*I 2 / | | / 1 + 3*I /|
x3 = – I*log| / / 10 */ -3 + I *sin|———| – I*/ 10 */ -3 + I *cos|———| * / ——————————– – ———————————- | + atan|—————————-|
/ 2 / 2 / / 10 10 / | / _________ |
| | / -1 ________||
|re| / ——- */ -3 + I ||
/ 1 + 3*I //

$$x_{3} = {atan}{left (frac{Im{left(sqrt{- frac{1}{1 + 3 i}} sqrt{-3 + i}right)}}{Re{left(sqrt{- frac{1}{1 + 3 i}} sqrt{-3 + i}right)}} right )} – i log{left (sqrt{- sqrt[4]{10} i sqrt{-3 + i} cos{left (frac{1}{2} {atan}{left (frac{1}{3} right )} right )} + sqrt[4]{10} sqrt{-3 + i} sin{left (frac{1}{2} {atan}{left (frac{1}{3} right )} right )}} sqrt{- frac{10^{frac{3}{4}} i}{10} sqrt{- frac{1}{1 + 3 i}} cos{left (frac{1}{2} {atan}{left (3 right )} right )} + frac{10^{frac{3}{4}}}{10} sqrt{- frac{1}{1 + 3 i}} sin{left (frac{1}{2} {atan}{left (3 right )} right )}} right )}$$

/ _______________________________________________________________________
| / _________ _________ | / / _________
| / 3/4 / -1 /atan(3) 3/4 / -1 /atan(3) | | | / -1 ________||
| _______________________________________________________________________ / 10 * / ——- *sin|——-| I*10 * / ——- *cos|——-| | |im| / ——- */ -3 + I ||
| / 4 ____ ________ /atan(1/3) 4 ____ ________ /atan(1/3) / / 1 + 3*I 2 / / 1 + 3*I 2 / | | / 1 + 3*I /|
x4 = pi – I*log| / / 10 */ -3 + I *sin|———| – I*/ 10 */ -3 + I *cos|———| * / ——————————– – ———————————- | + atan|—————————-|
/ 2 / 2 / / 10 10 / | / _________ |
| | / -1 ________||
|re| / ——- */ -3 + I ||
/ 1 + 3*I //

$$x_{4} = {atan}{left (frac{Im{left(sqrt{- frac{1}{1 + 3 i}} sqrt{-3 + i}right)}}{Re{left(sqrt{- frac{1}{1 + 3 i}} sqrt{-3 + i}right)}} right )} + pi – i log{left (sqrt{- sqrt[4]{10} i sqrt{-3 + i} cos{left (frac{1}{2} {atan}{left (frac{1}{3} right )} right )} + sqrt[4]{10} sqrt{-3 + i} sin{left (frac{1}{2} {atan}{left (frac{1}{3} right )} right )}} sqrt{- frac{10^{frac{3}{4}} i}{10} sqrt{- frac{1}{1 + 3 i}} cos{left (frac{1}{2} {atan}{left (3 right )} right )} + frac{10^{frac{3}{4}}}{10} sqrt{- frac{1}{1 + 3 i}} sin{left (frac{1}{2} {atan}{left (3 right )} right )}} right )}$$
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Численный ответ

x1 = -38.1627594521000

x2 = 577.267650097000

x3 = -3.92699081699000

x4 = 14.9225651046000

x5 = 90.3207887907000

x6 = -60.1539080272000

x7 = 34.0938715805000

x8 = -101.316363078000

x9 = -22.4547961841000

x10 = -73.0420291960000

x11 = 96.6039740979000

x12 = 62.0464549084000

x13 = -95.0331777711000

x14 = 74.6128255228000

x15 = -63.6172512352000

x16 = 77.7544181763000

x17 = -94.7114272167000

x18 = -82.1450566023000

x19 = 18.0641577581000

x20 = -50.7291300664000

x21 = 78.0761687307000

x22 = -29.0597320457000

x23 = 100.067317306000

x24 = 65.5097981164000

x25 = -13.3517687778000

x26 = -72.7202786416000

x27 = -75.8618712952000

x28 = 59.2266128092000

x29 = -85.6083998103000

x30 = 71.4712328692000

x31 = 80.8960108299000

x32 = 56.0850201556000

x33 = -0.785398163397000

x34 = 30.6305283725000

x35 = -47.9092879672000

x36 = 37.2354642341000

x37 = 197.456689567000

x38 = -97.8530198703000

x39 = -88.4282419095000

x40 = -6.74683291618000

x41 = -69.9004365424000

x42 = -0.463647609001000

x43 = 30.9522789269000

x44 = 40.0553063333000

x45 = 49.8018348484000

x46 = -16.1716108769000

x47 = 27.8106862733000

x48 = 36.9137136797000

x49 = -35.3429173529000

x50 = 68.3296402156000

x51 = 8.63937979737000

x52 = 52.6216769476000

x53 = -19.6349540849000

x54 = 15.2443156589000

x55 = 93.7841319987000

x56 = -53.8707227200000

x57 = -79.3252145031000

x58 = 58.9048622548000

x59 = -66.4370933344000

x60 = 81.2177613843000

x61 = 5.81953769818000

x62 = 43.5186495413000

x63 = -31.8795741449000

x64 = -57.3340659280000

x65 = -25.9181393921000

x66 = -9.88842556977000

x67 = 12.1027230054000

x68 = -41.6261026601000

x69 = 21.5275009661000

x70 = 84.0376034835000

x71 = 46.3384916404000

x72 = 24.3473430653000

x73 = -51.0508806208000

x74 = 71.7929834236000

x75 = -44.4459447593000

x76 = 128.019900634000

x77 = -28.7379814913000

x78 = -7.06858347058000

x79 = -91.8915851175000

x80 = 87.5009466915000

x81 = 2.35619449019000

   
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