Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^2-8*x+17=0
-
Equation 2-3(7+2x)=11
-
Equation x^2-2x+1=0
-
Equation 7+8x=-2x-5
- Express {x} in terms of y where:
- 7*x+19*y=12
- 17*x+20*y=-12
- 18*x-11*y=2
- 2*x-8*y=4
-
Identical expressions
- tg^ two (x- one)= zero
- tg squared (x minus 1) equally 0
- tg to the power of two (x minus one) equally zero
- tg2(x-1)=0
- tg2x-1=0
- tg²(x-1)=0
- tg to the power of 2(x-1)=0
- tg^2x-1=0
- tg^2(x-1)=O
-
Similar expressions
- tg^2(x+1)=0
tg^2(x-1)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\tan^{2}{\left(x - 1 \right)} = 0$$
transform
$$\tan^{2}{\left(x - 1 \right)} = 0$$
$$\tan^{2}{\left(x - 1 \right)} = 0$$
Do replacement
$$w = \tan{\left(x - 1 \right)}$$
Given the equation
$$\tan^{2}{\left(x - 1 \right)} = 0$$
so
$$\tan{\left(x - 1 \right)} = 0$$
Expand brackets in the left part
Move free summands (without w)
from left part to right part, we given:
$$\tan{\left(x - 1 \right)} + 1 = 1$$
This equation has no roots
do backward replacement
$$\tan{\left(x - 1 \right)} = w$$
Given the equation
$$\tan{\left(x - 1 \right)} = w$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x - 1 = \pi n + \operatorname{atan}{\left(w \right)}$$
Or
$$x - 1 = \pi n + \operatorname{atan}{\left(w \right)}$$
, where n - is a integer
Move
$$-1$$
to right part of the equation
with the opposite sign, in total:
$$x = \pi n + \operatorname{atan}{\left(w \right)} + 1$$
substitute w:
$$\tan^{2}{\left(x - 1 \right)} = 0$$
transform
$$\tan^{2}{\left(x - 1 \right)} = 0$$
$$\tan^{2}{\left(x - 1 \right)} = 0$$
Do replacement
$$w = \tan{\left(x - 1 \right)}$$
Given the equation
$$\tan^{2}{\left(x - 1 \right)} = 0$$
so
$$\tan{\left(x - 1 \right)} = 0$$
Expand brackets in the left part
tan-1+x = 0
Move free summands (without w)
from left part to right part, we given:
$$\tan{\left(x - 1 \right)} + 1 = 1$$
This equation has no roots
do backward replacement
$$\tan{\left(x - 1 \right)} = w$$
Given the equation
$$\tan{\left(x - 1 \right)} = w$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x - 1 = \pi n + \operatorname{atan}{\left(w \right)}$$
Or
$$x - 1 = \pi n + \operatorname{atan}{\left(w \right)}$$
, where n - is a integer
Move
$$-1$$
to right part of the equation
with the opposite sign, in total:
$$x = \pi n + \operatorname{atan}{\left(w \right)} + 1$$
substitute w:
Numerical answer
[src]
x1 = 16.707962954789
x2 = -17.8495557930769
x3 = 41.8407046221793
x4 = 98.3893721733986
x5 = 76.3982235930268
x6 = -5.28318562857736
x7 = -90.1061868645631
x8 = -96.3893719615832
x9 = -93.2477799637719
x10 = -80.6814082973509
x11 = -20.9911493135729
x12 = -42.9822979082595
x13 = -83.82300157382
x14 = 19.8495560411092
x15 = -74.3982233783165
x16 = -49.2654827958163
x17 = -27.2743342121104
x18 = 29.2743346759667
x19 = 26.1327414431435
x20 = -8.42477762755389
x21 = -58.6902597038896
x22 = 82.681408703946
x23 = -55.5486678895973
x24 = -68.1150382833435
x25 = 70.1150387116095
x26 = -11.5663707286158
x27 = 22.9911478740149
x28 = 4.14159281412036
x29 = 13.5663709563755
x30 = 79.5398167092837
x31 = -46.1238897021808
x32 = 92.1061876254523
x33 = -52.4070747948935
x34 = 63.8318532032527
x35 = -86.9645950995569
x36 = 10.4247778518281
x37 = -71.2566313797013
x38 = 44.9822964669671
x39 = 0.999999280509846
x40 = -99.5309650507317
x41 = 51.2654832725761
x42 = -36.6991111098542
x43 = 95.2477804679925
x44 = -24.1327411210597
x45 = 66.97344505939
x46 = -33.5575193090895
x47 = -61.8318529840814
x48 = -30.4159262113081
x49 = 38.6991115379946
x50 = 88.9645936513059
x51 = -39.8407043911242
x52 = 7.28318608004558
x53 = -77.5398164701434
x54 = 60.6902601210451
x55 = 57.5486681247873
x56 = -14.7079625152183
x57 = 73.2566318699064
x58 = 35.5575195404869
x59 = -64.9734465035777
x60 = 54.4070750126445
x61 = 32.4159264322466
x62 = -2.14159253996692
x63 = 85.823001784338
x63 = 85.823001784338