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- Equation:
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Equation √y^22/16y^16
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Identical expressions
- (cos(two x)-sqrt(2)*sin(x- one))/tg(x- one)= zero
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- ( co sinus of e of (two x) minus square root of (2) multiply by sinus of (x minus one)) divide by tg(x minus one) equally zero
- (cos(2x)-√(2)*sin(x-1))/tg(x-1)=0
- (cos(2x)-sqrt(2)sin(x-1))/tg(x-1)=0
- cos2x-sqrt2sinx-1/tgx-1=0
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- (cos(2x)-sqrt(2)*sin(x-1)) divide by tg(x-1)=0
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Similar expressions
- (cos(2x)-sqrt(2)*sin(x-1))/tg(x+1)=0
- (cos(2x)+sqrt(2)*sin(x-1))/tg(x-1)=0
- (cos(2x)-sqrt(2)*sin(x+1))/tg(x-1)=0
(cos(2x)-sqrt(2)*sin(x-1))/tg(x-1)=0 equation
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The solution
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___
cos(2*x) - \/ 2 *sin(x - 1)
--------------------------- = 0
tan(x - 1)
$$\frac{- \sqrt{2} \sin{\left(x - 1 \right)} + \cos{\left(2 x \right)}}{\tan{\left(x - 1 \right)}} = 0$$
Detail solution
Given the equation
$$\frac{- \sqrt{2} \sin{\left(x - 1 \right)} + \cos{\left(2 x \right)}}{\tan{\left(x - 1 \right)}} = 0$$
transform
$$\frac{- \sqrt{2} \sin{\left(x - 1 \right)} + 2 \cos^{2}{\left(x \right)} - \tan{\left(x - 1 \right)}}{\tan{\left(x - 1 \right)}} = 0$$
$$\frac{- \sqrt{2} \sin{\left(x - 1 \right)} + 2 \cos^{2}{\left(x \right)}}{\tan{\left(x - 1 \right)}} - 1 = 0$$
Do replacement
$$w = \sin{\left(x - 1 \right)}$$
Given the equation:
$$\frac{- \sqrt{2} \sin{\left(x - 1 \right)} + 2 \cos^{2}{\left(x \right)}}{\tan{\left(x - 1 \right)}} - 1 = 0$$
Use proportions rule:
From a1/b1 = a2/b2 should a1*b2 = a2*b1,
In this case
so we get the equation
$$- \sqrt{2} \sin{\left(x - 1 \right)} + 2 \cos^{2}{\left(x \right)} = \tan{\left(x - 1 \right)}$$
$$- \sqrt{2} \sin{\left(x - 1 \right)} + 2 \cos^{2}{\left(x \right)} = \tan{\left(x - 1 \right)}$$
Expand brackets in the left part
Expand brackets in the right part
Move free summands (without w)
from left part to right part, we given:
$$- \sqrt{2} \sin{\left(x - 1 \right)} + 2 \cos^{2}{\left(x \right)} + 1 = \tan{\left(x - 1 \right)} + 1$$
This equation has no roots
do backward replacement
$$\sin{\left(x - 1 \right)} = w$$
Given the equation
$$\sin{\left(x - 1 \right)} = w$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x - 1 = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x - 1 = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
Or
$$x - 1 = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x - 1 = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
, where n - is a integer
Move
$$-1$$
to right part of the equation
with the opposite sign, in total:
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)} + 1$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + 1 + \pi$$
substitute w:
$$\frac{- \sqrt{2} \sin{\left(x - 1 \right)} + \cos{\left(2 x \right)}}{\tan{\left(x - 1 \right)}} = 0$$
transform
$$\frac{- \sqrt{2} \sin{\left(x - 1 \right)} + 2 \cos^{2}{\left(x \right)} - \tan{\left(x - 1 \right)}}{\tan{\left(x - 1 \right)}} = 0$$
$$\frac{- \sqrt{2} \sin{\left(x - 1 \right)} + 2 \cos^{2}{\left(x \right)}}{\tan{\left(x - 1 \right)}} - 1 = 0$$
Do replacement
$$w = \sin{\left(x - 1 \right)}$$
Given the equation:
$$\frac{- \sqrt{2} \sin{\left(x - 1 \right)} + 2 \cos^{2}{\left(x \right)}}{\tan{\left(x - 1 \right)}} - 1 = 0$$
Use proportions rule:
From a1/b1 = a2/b2 should a1*b2 = a2*b1,
In this case
a1 = 2*cos(x)^2 - sqrt(2)*sin(-1 + x)
b1 = tan(-1 + x)
a2 = 1
b2 = 1
so we get the equation
$$- \sqrt{2} \sin{\left(x - 1 \right)} + 2 \cos^{2}{\left(x \right)} = \tan{\left(x - 1 \right)}$$
$$- \sqrt{2} \sin{\left(x - 1 \right)} + 2 \cos^{2}{\left(x \right)} = \tan{\left(x - 1 \right)}$$
Expand brackets in the left part
2*cosx^2 - sqrt2sin-1+x = tan(-1 + x)
Expand brackets in the right part
2*cosx^2 - sqrt2sin-1+x = tan-1+x
Move free summands (without w)
from left part to right part, we given:
$$- \sqrt{2} \sin{\left(x - 1 \right)} + 2 \cos^{2}{\left(x \right)} + 1 = \tan{\left(x - 1 \right)} + 1$$
This equation has no roots
do backward replacement
$$\sin{\left(x - 1 \right)} = w$$
Given the equation
$$\sin{\left(x - 1 \right)} = w$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x - 1 = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x - 1 = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
Or
$$x - 1 = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x - 1 = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
, where n - is a integer
Move
$$-1$$
to right part of the equation
with the opposite sign, in total:
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)} + 1$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + 1 + \pi$$
substitute w:
Numerical answer
[src]
x1 = -85.3937979737193
x2 = -69.6858347057703
x3 = -38.2699081698724
x4 = -47.6946861306418
x5 = -22.5619449019235
x6 = 80.2737551666594
x7 = 153.367243699105
x8 = -63.4026493985908
x9 = 77.9690200129499
x10 = -89.3722481271894
x11 = -17.9751282094757
x12 = 27.7035375555132
x13 = -51.6731362841119
x14 = -88.5353906273091
x15 = -28.845130209103
x16 = 2.5707963267949
x17 = -3.71238898038469
x18 = 4.87553148050438
x19 = -95.655433434369
x20 = 71.6858347057703
x21 = 36.2914580164023
x22 = -53.9778714378214
x23 = -35.1283155162826
x24 = 96.8185759344887
x25 = 93.6769832808989
x26 = 92.8401257810186
x27 = 48.8578286307615
x28 = -72.8274273593601
x29 = -13.9740244410344
x30 = 21.4203522483337
x31 = -9.99557428756428
x32 = 42.5746433235819
x33 = 49.6946861306418
x34 = -41.4115008234622
x35 = 32.290354247961
x36 = 26.0071689407814
x37 = -75.9690200129499
x38 = -64.2395068984711
x39 = -25.7035375555132
x40 = -7.69083913385479
x41 = 86.556940473839
x42 = 65.4026493985908
x43 = 11.9955742875643
x44 = -20.257209748214
x45 = -97.9601685880785
x46 = -45.3899509769323
x47 = -82.2522053201295
x48 = -66.5442420521806
x49 = 90.5353906273091
x50 = 76.2726513982181
x51 = -11.6919429022961
x52 = -32.8235803625731
x53 = -61.9574253597328
x54 = 15.1371669411541
x55 = 69.9894660910385
x56 = 43.4115008234622
x57 = -91.6769832808989
x58 = 62.261056745001
x59 = 87.3937979737193
x60 = -31.9867228626928
x61 = -57.9563215912915
x62 = 52.8362787842316
x63 = -60.261056745001
x64 = 59.1194640914112
x65 = -44.553093477052
x66 = 5.71238898038469
x67 = 84.2522053201295
x68 = 46.553093477052
x69 = 73.9905698594798
x70 = 33.9867228626928
x71 = 99.9601685880785
x72 = 30.0082727092227
x73 = 40.2699081698724
x74 = 8.85398163397448
x75 = -101.938618741549
x76 = 18.2787595947439
x77 = 55.9778714378214
x78 = -79.1106126665397
x79 = 23.7250874020431
x80 = -1.4076538266752
x81 = -0.570796326794897
x81 = -0.570796326794897