Mister Exam
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Equation x^2-8x+15=0
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Identical expressions
- tan(x)+ two *cot(x)- three = zero
- tangent of (x) plus 2 multiply by cotangent of (x) minus 3 equally 0
- tangent of (x) plus two multiply by cotangent of (x) minus three equally zero
- tan(x)+2cot(x)-3=0
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Similar expressions
- tan(x)-2*cot(x)-3=0
- tan(x)+2*cot(x)+3=0
tan(x)+2*cot(x)-3=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
tan(x) + 2*cot(x) - 3 = 0
$$\tan{\left(x \right)} + 2 \cot{\left(x \right)} - 3 = 0$$
Detail solution
Given the equation:
$$\tan{\left(x \right)} + 2 \cot{\left(x \right)} - 3 = 0$$
Transform
$$\tan{\left(x \right)} + 2 \cot{\left(x \right)} - 3 = 0$$
$$\frac{\left(\tan{\left(x \right)} - 2\right) \left(\tan{\left(x \right)} - 1\right)}{\tan{\left(x \right)}} = 0$$
Consider each factor separately
$$\tan{\left(x \right)} = 0$$
- this is the simplest trigonometric equation
We get:
$$\tan{\left(x \right)} = 0$$
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(0 \right)}$$
Or
$$x = \pi n$$
, where n - is a integer
$$\tan{\left(x \right)} - 1 = 0$$
- this is the simplest trigonometric equation
Move $-1$ to right part of the equation
with the change of sign in $-1$
We get:
$$\tan{\left(x \right)} = 1$$
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(1 \right)}$$
Or
$$x = \pi n + \frac{\pi}{4}$$
, where n - is a integer
$$\tan{\left(x \right)} - 2 = 0$$
- this is the simplest trigonometric equation
Move $-2$ to right part of the equation
with the change of sign in $-2$
We get:
$$\tan{\left(x \right)} = 2$$
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(2 \right)}$$
Or
$$x = \pi n + \operatorname{atan}{\left(2 \right)}$$
, where n - is a integer
The final answer:
$$x_{1} = \pi n$$
$$x_{2} = \pi n + \frac{\pi}{4}$$
$$x_{3} = \pi n + \operatorname{atan}{\left(2 \right)}$$
$$\tan{\left(x \right)} + 2 \cot{\left(x \right)} - 3 = 0$$
Transform
$$\tan{\left(x \right)} + 2 \cot{\left(x \right)} - 3 = 0$$
$$\frac{\left(\tan{\left(x \right)} - 2\right) \left(\tan{\left(x \right)} - 1\right)}{\tan{\left(x \right)}} = 0$$
Consider each factor separately
Step
$$\tan{\left(x \right)} = 0$$
- this is the simplest trigonometric equation
We get:
$$\tan{\left(x \right)} = 0$$
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(0 \right)}$$
Or
$$x = \pi n$$
, where n - is a integer
Step
$$\tan{\left(x \right)} - 1 = 0$$
- this is the simplest trigonometric equation
Move $-1$ to right part of the equation
with the change of sign in $-1$
We get:
$$\tan{\left(x \right)} = 1$$
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(1 \right)}$$
Or
$$x = \pi n + \frac{\pi}{4}$$
, where n - is a integer
Step
$$\tan{\left(x \right)} - 2 = 0$$
- this is the simplest trigonometric equation
Move $-2$ to right part of the equation
with the change of sign in $-2$
We get:
$$\tan{\left(x \right)} = 2$$
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(2 \right)}$$
Or
$$x = \pi n + \operatorname{atan}{\left(2 \right)}$$
, where n - is a integer
The final answer:
$$x_{1} = \pi n$$
$$x_{2} = \pi n + \frac{\pi}{4}$$
$$x_{3} = \pi n + \operatorname{atan}{\left(2 \right)}$$
Rapid solution
[src]
pi
x_1 = --
4
$$x_{1} = \frac{\pi}{4}$$
x_2 = atan(2)
$$x_{2} = \operatorname{atan}{\left(2 \right)}$$
Sum and product of roots
[src]
sum
pi -- + atan(2) 4
$$\left(\frac{\pi}{4}\right) + \left(\operatorname{atan}{\left(2 \right)}\right)$$
=
pi -- + atan(2) 4
$$\frac{\pi}{4} + \operatorname{atan}{\left(2 \right)}$$
product
pi -- * atan(2) 4
$$\left(\frac{\pi}{4}\right) * \left(\operatorname{atan}{\left(2 \right)}\right)$$
=
pi*atan(2)
----------
4
$$\frac{\pi \operatorname{atan}{\left(2 \right)}}{4}$$
Numerical answer
[src]
x1 = 120.487669554206
x2 = -93.4623814442964
x3 = -71.4712328691678
x4 = -5.49778714378214
x5 = -84.037603483527
x6 = 79.6469650575389
x7 = 44.7676953136546
x8 = -80.8960108299372
x9 = -43.1968989868597
x10 = -64.8662970075916
x11 = 10.2101761241668
x12 = 22.776546738526
x13 = 57843.7893360587
x14 = -52.2999263932324
x15 = 85.9301503647185
x16 = -99.7455667514759
x17 = -68.0078896611814
x18 = 82.4668071567321
x19 = -11.7809724509617
x20 = 98.174770424681
x21 = -46.0167410860528
x22 = -36.9137136796801
x23 = -87.1791961371168
x24 = -1290.40918246201
x25 = 66.7588438887831
x26 = -39.7335557788732
x27 = 92.2133356718981
x28 = -62.0464549083984
x29 = 63.93900178959
x30 = -27.4889357189107
x31 = -77.7544181763474
x32 = -30.6305283725005
x33 = -52.621676947629
x34 = 76.1836218495525
x35 = -21.2057504117311
x36 = -74.2910749683609
x37 = 16.4933614313464
x38 = 10.5319266785635
x39 = 38.8062605608716
x40 = 69.9004365423729
x41 = 70.2221870967695
x42 = 41.9478532144614
x43 = -65.1880475619882
x44 = -46.3384916404494
x45 = 85.6083998103219
x46 = 51.0508806208341
x47 = -24.0255925109243
x48 = 19.9567046393328
x49 = -30.3087778181038
x50 = 26.2398899465124
x51 = 54.5142238288206
x52 = -14.6008145501549
x53 = -128.019900633784
x54 = -5.1760365893855
x55 = -96.2822235434895
x56 = 60.4756585816035
x57 = -74.6128255227576
x58 = 4.24874137138388
x59 = 48.231038521641
x60 = -89.9990382363099
x61 = 32.2013246992954
x62 = 91.8915851175014
x63 = -49.4800842940392
x64 = 88.7499924639117
x65 = -8.31762924297529
x66 = -58.9048622548086
x67 = -55.7632696012188
x68 = -17.7424072037447
x69 = 16.8151119857431
x70 = 13.6735193321533
x71 = 214.413698607503
x72 = -33.7721210260903
x73 = 38.484510006475
x74 = -162.577419823272
x75 = -61.7247043540018
x76 = 54.1924732744239
x77 = -115.453530019425
x78 = -2.0344439357957
x79 = -18.0641577581413
x79 = -18.0641577581413
The graph