Mister Exam
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How to use it?
- Equation:
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Equation x^2-2x+1=0
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Equation x^4+4=0
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Equation 3(x+3)=2x+5
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Identical expressions
- -tan(x/ two)= one / two *ln(two)
- minus tangent of (x divide by 2) equally 1 divide by 2 multiply by ln(2)
- minus tangent of (x divide by two) equally one divide by two multiply by ln(two)
- -tan(x/2)=1/2ln(2)
- -tanx/2=1/2ln2
- -tan(x divide by 2)=1 divide by 2*ln(2)
-
Similar expressions
- (1/2)*ln(2*y+1)=C-ln(cos(x))
- tan(x/2)=1/2*ln(2)
-tan(x/2)=1/2*ln(2) equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
/x\ log(2)
-tan|-| = ------
\2/ 2
$$- \tan{\left(\frac{x}{2} \right)} = \frac{\log{\left(2 \right)}}{2}$$
Detail solution
Given the equation
$$- \tan{\left(\frac{x}{2} \right)} = \frac{\log{\left(2 \right)}}{2}$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\tan{\left(\frac{x}{2} \right)} = - \frac{\log{\left(2 \right)}}{2}$$
This equation is transformed to
$$\frac{x}{2} = \pi n + \operatorname{atan}{\left(- \frac{\log{\left(2 \right)}}{2} \right)}$$
Or
$$\frac{x}{2} = \pi n - \operatorname{atan}{\left(\frac{\log{\left(2 \right)}}{2} \right)}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{2}$$
we get the answer:
$$x_{1} = 2 \pi n - 2 \operatorname{atan}{\left(\frac{\log{\left(2 \right)}}{2} \right)}$$
$$- \tan{\left(\frac{x}{2} \right)} = \frac{\log{\left(2 \right)}}{2}$$
- this is the simplest trigonometric equation
Divide both parts of the equation by -1
The equation is transformed to
$$\tan{\left(\frac{x}{2} \right)} = - \frac{\log{\left(2 \right)}}{2}$$
This equation is transformed to
$$\frac{x}{2} = \pi n + \operatorname{atan}{\left(- \frac{\log{\left(2 \right)}}{2} \right)}$$
Or
$$\frac{x}{2} = \pi n - \operatorname{atan}{\left(\frac{\log{\left(2 \right)}}{2} \right)}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{2}$$
we get the answer:
$$x_{1} = 2 \pi n - 2 \operatorname{atan}{\left(\frac{\log{\left(2 \right)}}{2} \right)}$$
Rapid solution
[src]
/log(2)\
x1 = -2*atan|------|
\ 2 /
$$x_{1} = - 2 \operatorname{atan}{\left(\frac{\log{\left(2 \right)}}{2} \right)}$$
x1 = -2*atan(log(2)/2)
Sum and product of roots
[src]
sum
/log(2)\
-2*atan|------|
\ 2 /
$$- 2 \operatorname{atan}{\left(\frac{\log{\left(2 \right)}}{2} \right)}$$
=
/log(2)\
-2*atan|------|
\ 2 /
$$- 2 \operatorname{atan}{\left(\frac{\log{\left(2 \right)}}{2} \right)}$$
product
/log(2)\
-2*atan|------|
\ 2 /
$$- 2 \operatorname{atan}{\left(\frac{\log{\left(2 \right)}}{2} \right)}$$
=
/log(2)\
-2*atan|------|
\ 2 /
$$- 2 \operatorname{atan}{\left(\frac{\log{\left(2 \right)}}{2} \right)}$$
-2*atan(log(2)/2)
Numerical answer
[src]
x1 = 18.1823177547056
x2 = 30.7486883690648
x3 = 49.5982442906035
x4 = 81.0141708265015
x5 = 99.8637267480402
x6 = 11.899132447526
x7 = 5.61594714034644
x8 = -44.6495353170903
x9 = -63.499091238629
x10 = -0.667238166833151
x11 = -94.9150177745269
x12 = 55.8814295977831
x13 = 62.1646149049627
x14 = -19.5167940883719
x15 = 24.4655030618852
x16 = -50.9327206242698
x17 = -88.6318324673474
x18 = -32.0831647027311
x19 = -13.2336087811923
x20 = -57.2159059314494
x21 = 93.5805414408606
x22 = -82.3486471601678
x23 = 87.2973561336811
x24 = -76.0654618529882
x25 = 37.0318736762444
x26 = -38.3663500099107
x27 = 68.4478002121423
x28 = 43.315058983424
x29 = -6.95042347401274
x30 = -25.7999793955515
x31 = -101.198203081707
x32 = 74.7309855193219
x33 = -69.7822765458086
x33 = -69.7822765458086