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cos2x-1=0 equation

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cos(2*x) - 1 = 0

\cos{\left(2 x \right)} - 1 = 0

Simplify

Detail solution

Given the equation

\cos{\left(2 x \right)} - 1 = 0

- this is the simplest trigonometric equation

Move -1 to right part of the equation

with the change of sign in -1

We get:

\cos{\left(2 x \right)} - 1 + 1 = 1

This equation is transformed to

2 x = \pi n + \operatorname{acos}{\left(1 \right)}

2 x = \pi n - \pi + \operatorname{acos}{\left(1 \right)}

2 x = \pi n

2 x = \pi n - \pi

, where n - is a integer
Divide both parts of the equation by

2

we get the answer:

x_{1} = \frac{\pi n}{2}

x_{2} = \frac{\pi n}{2} - \frac{\pi}{2}

The graph

Plot the graph f1(x)

Plot the graph f2(x)

Sum and product of roots [src]

sum

0 + 0 + pi

\left(0 + 0\right) + \pi

pi

\pi

product

1*0*pi

1 \cdot 0 \pi

0

Rapid solution [src]

x1 = 0

x_{1} = 0

Simplify

x2 = pi

x_{2} = \pi

Simplify

Numerical answer [src]

x1 = 6.28318528425126

x2 = -40.8407042660168

x3 = 21.9911485851964

x4 = 69.1150385885879

x5 = 47.123890018392

x6 = -1734.15914475848

x7 = 75.3982239388525

x8 = 56.5486676091327

x9 = -40.8407046898283

x10 = 81.6814091761104

x11 = -31.4159267959754

x12 = -65.9734457650176

x13 = 3.14159244884412

x14 = 69.1150381602162

x15 = -91.106187201329

x16 = 47.123889589354

x17 = -91.1061872003049

x18 = -69.1150386737158

x19 = -3.14159311568248

x20 = 31.4159267865366

x21 = -59.6902604576401

x22 = -84.8230018263493

x23 = -47.1238900492539

x24 = 0.0

x25 = 91.1061867314459

x26 = -106.814150357553

x27 = 62.8318524523063

x28 = 9.42477859080277

x29 = -84.82300141007

x30 = 100.530964766599

x31 = -69.1150386253436

x32 = -21.9911485864515

x33 = 25.1327414478072

x34 = -6371388.6625218

x35 = -18.8495556944209

x36 = 97.3893727097471

x37 = -9.42477812668337

x38 = 9.42477821024198

x39 = 25.1327410188866

x40 = -34.5575189701076

x41 = -97.3893724403711

x42 = -62.8318528379059

x43 = 62.8318528326557

x44 = 12.5663704518704

x45 = -15.7079632965264

x46 = -87.9645943587732

x47 = -50.2654822953391

x48 = 34.5575190304759

x49 = 65.9734457528975

x50 = 75.3982241944528

x51 = 37.6991120192083

x52 = 40.8407042560881

x53 = -53.4070752836338

x54 = 28.2743338652012

x55 = -72.2566308741333

x56 = 78.5398161878405

x57 = -3.14159289677385

x58 = -12.5663703661411

x59 = 91.1061871583643

x60 = 40.840703919946

x61 = -81.6814090380061

x62 = -62.8318532583801

x63 = -31.4159267051849

x64 = -78.5398160958028

x65 = -18.8495561207399

x66 = 18.8495556796107

x67 = -12.5663700417108

x68 = -34.5575189426108

x69 = 84.8230010166547

x70 = -75.3982238620294

x71 = 87.9645943357576

x72 = 31.4159271479423

x73 = -25.132741632083

x74 = -43.9822971745789

x75 = -37.6991118771514

x76 = 43.982297169427

x77 = -47.123890151099

x78 = -25.132741473063

x79 = 59.6902605976901

x80 = -28.2743337166085

x81 = 53.4070753627408

x82 = 15.7079634406648

x83 = 53.4070756765307

x84 = -56.5486675191652

x85 = 94.2477796093525

x86 = -100.530964672522

x87 = 97.3893725148693

x88 = -6.28318513794069

x89 = 84.8230014093114

x90 = -94.2477794529919

x91 = 3.14159287686128

x92 = 18.8495554002244

x93 = 72.256631027719

x94 = 50.2654824463473

x94 = 50.2654824463473

The graph