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Equation:
Equation x^2+5x+6=0
Equation 5x+12=8x+30
Equation 81*x^3+18*x^2+x=0
Equation x(x^2+2x+1)=6(x+1)
Express {x} in terms of y where:
-14*x-8*y=20
8*x+6*y=20
-11*x-19*y=14
-16*x+10*y=-11
Derivative of:
2sin2x
Integral of d{x}:
2sin2x
Identical expressions
one +3sin²x=2sin2x
1 plus 3 sinus of ²x equally 2 sinus of 2x
one plus 3 sinus of ²x equally 2 sinus of 2x
Similar expressions
1-3sin²x=2sin2x
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2*sin(2*x)-1=0
2*sin(2*x)-cos(x)*(x)=(sqrt(3))*sin(x)

1+3sin²x=2sin2x equation

The teacher will be very surprised to see your correct solution 😉

The solution

You have entered [src]

         2                
1 + 3*sin (x) = 2*sin(2*x)

$$3 \sin^{2}{\left(x \right)} + 1 = 2 \sin{\left(2 x \right)}$$

Simplify

The graph

Plot the graph f1(x)

Plot the graph f2(x)

Rapid solution [src]

             /log(5)      /  ___\\            
x1 = -pi + I*|------ - log\\/ 5 /| + atan(1/2)
             \  2                /

$$x_{1} = - \pi + \operatorname{atan}{\left(\frac{1}{2} \right)} + i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)$$

       /log(5)      /  ___\\            
x2 = I*|------ - log\\/ 5 /| + atan(1/2)
       \  2                /

$$x_{2} = \operatorname{atan}{\left(\frac{1}{2} \right)} + i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)$$

x2 = atan(1/2) + i*(-log(sqrt(5)) + log(5)/2)

Sum and product of roots [src]

sum

        /log(5)      /  ___\\                 /log(5)      /  ___\\            
-pi + I*|------ - log\\/ 5 /| + atan(1/2) + I*|------ - log\\/ 5 /| + atan(1/2)
        \  2                /                 \  2                /

$$\left(- \pi + \operatorname{atan}{\left(\frac{1}{2} \right)} + i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)\right) + \left(\operatorname{atan}{\left(\frac{1}{2} \right)} + i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)\right)$$

                        /log(5)      /  ___\\
-pi + 2*atan(1/2) + 2*I*|------ - log\\/ 5 /|
                        \  2                /

$$- \pi + 2 \operatorname{atan}{\left(\frac{1}{2} \right)} + 2 i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)$$

product

/        /log(5)      /  ___\\            \ /  /log(5)      /  ___\\            \
|-pi + I*|------ - log\\/ 5 /| + atan(1/2)|*|I*|------ - log\\/ 5 /| + atan(1/2)|
\        \  2                /            / \  \  2                /            /

$$\left(\operatorname{atan}{\left(\frac{1}{2} \right)} + i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)\right) \left(- \pi + \operatorname{atan}{\left(\frac{1}{2} \right)} + i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)\right)$$

(-pi + atan(1/2))*atan(1/2)

$$\left(- \pi + \operatorname{atan}{\left(\frac{1}{2} \right)}\right) \operatorname{atan}{\left(\frac{1}{2} \right)}$$

(-pi + atan(1/2))*atan(1/2)

Numerical answer [src]

x1 = 91.5698347820202

x2 = 50.7291298499194

x3 = -56.0850201846647

x4 = -40.3770566846988

x5 = -90.6425390919457

x6 = 100.994612275511

x7 = -18.3859081067509

x8 = -59.2266130367289

x9 = 25.596389048953

x10 = -30.9522787714231

x11 = -21.5275010891603

x12 = -68.6513905620246

x13 = -100.067317246335

x14 = -46.6602419381551

x15 = 35.0211665530579

x16 = -56.0850200842809

x17 = -24.6690933628312

x18 = -2.67794494964284

x19 = -46.6602420281656

x20 = -43.5186496682519

x21 = -12.1027229230545

x22 = -27.8106862171249

x23 = -96.9257248863081

x24 = 41.3043521413617

x25 = 16.1716109577973

x26 = -87.5009468262829

x27 = -15.2443158822842

x28 = 79.0034637011817

x29 = -74.9345763136722

x30 = -43.5186496987085

x31 = -30.9522791676501

x32 = -74.9345759040321

x33 = 28.7379812724486

x34 = 41.3043523624219

x35 = 57.012315483469

x36 = -68.6513905135924

x37 = 47.5875376267079

x38 = 19.3132035944434

x39 = 75.8618713975565

x40 = -62.3682052627098

x41 = 69.5786862043972

x42 = -49.8018348025009

x43 = 79.0034640445039

x44 = -90.6425390891399

x45 = 85.2866495119495

x46 = -8.96113059429183

x47 = 22.4547960691769

x48 = 88.4282418070787

x49 = 85.286649242635

x50 = 66.4370932277241

x51 = -84.3593538407837

x52 = 44.4459446484238

x53 = 19.3132037874613

x54 = 9.88842565730505

x55 = -71.7929833869144

x56 = -34.0938715035767

x57 = 53.8707228175982

x58 = -5.81953763049741

x59 = -52.9434273373617

x60 = -81.2177616138394

x61 = -78.0761686651908

x62 = -84.359354409878

x63 = 63.2955009372529

x64 = -24.6690934906105

x65 = 3.6052404711332

x66 = -2.67794478762447

x67 = 38.1627595483743

x68 = -93.7841319705718

x69 = 6.74683269504696

x70 = -52.9434277407813

x71 = 50.7291300369108

x72 = 60.1539081421637

x73 = 13.0300183579683

x74 = -37.2354644595433

x75 = 35.0211669212533

x76 = 63.2955006908421

x77 = 57.0123151270279

x78 = -96.9257244713711

x79 = 13.0300179792812

x80 = 72.720278427458

x81 = 97.8530199774025

x82 = 31.8795742375181

x83 = -8.96113020628676

x84 = 94.711427005063

x85 = 82.1450567405327

x86 = -65.5097982472926

x87 = 0.463647489982435

x87 = 0.463647489982435

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Identical expressions

Similar expressions

1+3sin²x=2sin2x equation

Numerical solution:

The solution