Mister Exam
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- Equation:
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Equation (x-11)/(x-6)=11/16
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Equation -(-y+4)+2*y+1=0
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Equation 8x−5(x+1)=−2x.
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Identical expressions
- y=(one \sina)*(ln(tgx+ctgx))
- y equally (1\ sinus of a) multiply by (ln(tgx plus ctgx))
- y equally (one \ sinus of a) multiply by (ln(tgx plus ctgx))
- y=(1\sina)(ln(tgx+ctgx))
- y=1\sinalntgx+ctgx
-
Similar expressions
- y=(1\sina)*(ln(tgx-ctgx))
y=(1\sina)*(ln(tgx+ctgx)) equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
log(tan(x) + cot(x))
y = --------------------
sin(a)
$$y = \frac{\log{\left(\tan{\left(x \right)} + \cot{\left(x \right)} \right)}}{\sin{\left(a \right)}}$$
Detail solution
Given the equation:
$$y = \frac{\log{\left(\tan{\left(x \right)} + \cot{\left(x \right)} \right)}}{\sin{\left(a \right)}}$$
transform:
$$y = \frac{\log{\left(\tan{\left(x \right)} + \cot{\left(x \right)} \right)}}{\sin{\left(a \right)}}$$
Expand brackets in the right part
We get the answer: y = log(cot(x) + tan(x))/sin(a)
$$y = \frac{\log{\left(\tan{\left(x \right)} + \cot{\left(x \right)} \right)}}{\sin{\left(a \right)}}$$
transform:
$$y = \frac{\log{\left(\tan{\left(x \right)} + \cot{\left(x \right)} \right)}}{\sin{\left(a \right)}}$$
Expand brackets in the right part
y = logcot+x + tanx)/sina
We get the answer: y = log(cot(x) + tan(x))/sin(a)
The graph
Rapid solution
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/log(cot(x) + tan(x))\ /log(cot(x) + tan(x))\
y1 = I*im|--------------------| + re|--------------------|
\ sin(a) / \ sin(a) /
$$y_{1} = \operatorname{re}{\left(\frac{\log{\left(\tan{\left(x \right)} + \cot{\left(x \right)} \right)}}{\sin{\left(a \right)}}\right)} + i \operatorname{im}{\left(\frac{\log{\left(\tan{\left(x \right)} + \cot{\left(x \right)} \right)}}{\sin{\left(a \right)}}\right)}$$
y1 = re(log(tan(x) + cot(x))/sin(a)) + i*im(log(tan(x) + cot(x))/sin(a))
Sum and product of roots
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sum
/log(cot(x) + tan(x))\ /log(cot(x) + tan(x))\
I*im|--------------------| + re|--------------------|
\ sin(a) / \ sin(a) /
$$\operatorname{re}{\left(\frac{\log{\left(\tan{\left(x \right)} + \cot{\left(x \right)} \right)}}{\sin{\left(a \right)}}\right)} + i \operatorname{im}{\left(\frac{\log{\left(\tan{\left(x \right)} + \cot{\left(x \right)} \right)}}{\sin{\left(a \right)}}\right)}$$
=
/log(cot(x) + tan(x))\ /log(cot(x) + tan(x))\
I*im|--------------------| + re|--------------------|
\ sin(a) / \ sin(a) /
$$\operatorname{re}{\left(\frac{\log{\left(\tan{\left(x \right)} + \cot{\left(x \right)} \right)}}{\sin{\left(a \right)}}\right)} + i \operatorname{im}{\left(\frac{\log{\left(\tan{\left(x \right)} + \cot{\left(x \right)} \right)}}{\sin{\left(a \right)}}\right)}$$
product
/log(cot(x) + tan(x))\ /log(cot(x) + tan(x))\
I*im|--------------------| + re|--------------------|
\ sin(a) / \ sin(a) /
$$\operatorname{re}{\left(\frac{\log{\left(\tan{\left(x \right)} + \cot{\left(x \right)} \right)}}{\sin{\left(a \right)}}\right)} + i \operatorname{im}{\left(\frac{\log{\left(\tan{\left(x \right)} + \cot{\left(x \right)} \right)}}{\sin{\left(a \right)}}\right)}$$
=
/log(cot(x) + tan(x))\ /log(cot(x) + tan(x))\
I*im|--------------------| + re|--------------------|
\ sin(a) / \ sin(a) /
$$\operatorname{re}{\left(\frac{\log{\left(\tan{\left(x \right)} + \cot{\left(x \right)} \right)}}{\sin{\left(a \right)}}\right)} + i \operatorname{im}{\left(\frac{\log{\left(\tan{\left(x \right)} + \cot{\left(x \right)} \right)}}{\sin{\left(a \right)}}\right)}$$
i*im(log(cot(x) + tan(x))/sin(a)) + re(log(cot(x) + tan(x))/sin(a))