Mister Exam

Lang:

Other calculators

How to use it?
Equation:
Equation ||x|-4|=5
Equation 3*x-7/8-x-3/6=1
Equation -2x^2+x+7=-x^2+5x+(-2-x^2)
Equation 1-10x=5x+10
Express {x} in terms of y where:
-4*x-20*y=10
1*x+18*y=-5
-15*x+11*y=-7
5*x+20*y=-4
Derivative of:
tgx+ctgx
Identical expressions
three +2sin2x=tgx+ctgx
3 plus 2 sinus of 2x equally tgx plus ctgx
three plus 2 sinus of 2x equally tgx plus ctgx
Similar expressions
tg(x)+ctg(x)=-2
3+2sin2x=tgx-ctgx
2*sqrt(3)+2*sin(2x)=3+2*sqrt(3)*sin(x)
3-2sin2x=tgx+ctgx

3+2sin2x=tgx+ctgx equation

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

The solution

You have entered [src]

3 + 2*sin(2*x) = tan(x) + cot(x)

$$2 \sin{\left(2 x \right)} + 3 = \tan{\left(x \right)} + \cot{\left(x \right)}$$

Simplify

The graph

Plot the graph f1(x)

Plot the graph f2(x)

Sum and product of roots [src]

sum

                /    /        ___\\       /    /        ___\\       /    /        ___\\       /    /        ___\\
pi   5*pi       |    |1   I*\/ 3 ||       |    |1   I*\/ 3 ||       |    |1   I*\/ 3 ||       |    |1   I*\/ 3 ||
-- + ---- + - re|atan|- - -------|| - I*im|atan|- - -------|| + - re|atan|- + -------|| - I*im|atan|- + -------||
12    12        \    \2      2   //       \    \2      2   //       \    \2      2   //       \    \2      2   //

$$\left(- \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}\right) + \left(\left(\frac{\pi}{12} + \frac{5 \pi}{12}\right) + \left(- \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}\right)\right)$$

       /    /        ___\\     /    /        ___\\       /    /        ___\\       /    /        ___\\
pi     |    |1   I*\/ 3 ||     |    |1   I*\/ 3 ||       |    |1   I*\/ 3 ||       |    |1   I*\/ 3 ||
-- - re|atan|- + -------|| - re|atan|- - -------|| - I*im|atan|- + -------|| - I*im|atan|- - -------||
2      \    \2      2   //     \    \2      2   //       \    \2      2   //       \    \2      2   //

$$- \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} - \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)} + \frac{\pi}{2} - i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}$$

product

        /    /    /        ___\\       /    /        ___\\\ /    /    /        ___\\       /    /        ___\\\
pi 5*pi |    |    |1   I*\/ 3 ||       |    |1   I*\/ 3 ||| |    |    |1   I*\/ 3 ||       |    |1   I*\/ 3 |||
--*----*|- re|atan|- - -------|| - I*im|atan|- - -------|||*|- re|atan|- + -------|| - I*im|atan|- + -------|||
12  12  \    \    \2      2   //       \    \2      2   /// \    \    \2      2   //       \    \2      2   ///

$$\frac{\pi}{12} \frac{5 \pi}{12} \left(- \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}\right) \left(- \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}\right)$$

      /    /    /        ___\\     /    /        ___\\\ /    /    /        ___\\     /    /        ___\\\
    2 |    |    |1   I*\/ 3 ||     |    |1   I*\/ 3 ||| |    |    |1   I*\/ 3 ||     |    |1   I*\/ 3 |||
5*pi *|I*im|atan|- + -------|| + re|atan|- + -------|||*|I*im|atan|- - -------|| + re|atan|- - -------|||
      \    \    \2      2   //     \    \2      2   /// \    \    \2      2   //     \    \2      2   ///
---------------------------------------------------------------------------------------------------------
                                                   144

$$\frac{5 \pi^{2} \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}\right)}{144}$$

5*pi^2*(i*im(atan(1/2 + i*sqrt(3)/2)) + re(atan(1/2 + i*sqrt(3)/2)))*(i*im(atan(1/2 - i*sqrt(3)/2)) + re(atan(1/2 - i*sqrt(3)/2)))/144

Rapid solution [src]

     pi
x1 = --
     12

$$x_{1} = \frac{\pi}{12}$$

     5*pi
x2 = ----
      12

$$x_{2} = \frac{5 \pi}{12}$$

         /    /        ___\\       /    /        ___\\
         |    |1   I*\/ 3 ||       |    |1   I*\/ 3 ||
x3 = - re|atan|- - -------|| - I*im|atan|- - -------||
         \    \2      2   //       \    \2      2   //

$$x_{3} = - \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}$$

         /    /        ___\\       /    /        ___\\
         |    |1   I*\/ 3 ||       |    |1   I*\/ 3 ||
x4 = - re|atan|- + -------|| - I*im|atan|- + -------||
         \    \2      2   //       \    \2      2   //

$$x_{4} = - \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}$$

x4 = -re(atan(1/2 + sqrt(3)*i/2)) - i*im(atan(1/2 + sqrt(3)*i/2))

Numerical answer [src]

x1 = 235.881248407034

x2 = 155.247036964896

x3 = -83.5140047079287

x4 = -89.7971900151083

x5 = -87.7027949127151

x6 = 7.59218224617533

x7 = -50.0036830696375

x8 = 32.7249234748937

x9 = 42.1497014356631

x10 = -103.410758180664

x11 = -65.7116463375865

x12 = 88.2263936883134

x13 = -6.02138591938044

x14 = -96.0803753222878

x15 = 48.4328867428426

x16 = 98.6983692002793

x17 = -39.5317075576716

x18 = 59.9520598060052

x19 = -30.1069295969022

x20 = -45.8148928648512

x21 = 86.1319985859202

x22 = 4.45058959258554

x23 = -71.9948316447661

x24 = 37.9609112308767

x25 = 51.5744793964324

x26 = 92.4151838930998

x27 = 13.8753675533549

x28 = -55.2396708256205

x29 = 64.1408500107916

x30 = 81.9432083811338

x31 = -21.7293491873294

x32 = 44.2440965380563

x33 = -67.8060414399797

x34 = 72.5184304203644

x35 = -23.8237442897226

x36 = -28.012534494509

x37 = 22.2529479629277

x38 = 1549.06697760757

x39 = -43.720497762458

x40 = -18.5877565337396

x41 = 66.2352451131848

x42 = -2013.49909156326

x43 = -46.8620904160477

x44 = -86.6555973615185

x45 = 15.9697626557481

x46 = -36.3901149040818

x47 = -8.11578102177363

x48 = 70.4240353179712

x49 = 47.3856891916461

x50 = -93.9859802198946

x51 = 29.5833308213039

x52 = 20.1585528605345

x53 = 154.199839413699

x54 = -17.540558982543

x55 = -1.83259571459405

x56 = 39.0081087820733

x57 = -52.0980781720307

x58 = -74.0892267471593

x59 = -12.30457122656

x59 = -12.30457122656

Other calculators

How to use it?

Identical expressions

Similar expressions

3+2sin2x=tgx+ctgx equation

Numerical solution:

The solution