Mister Exam
How do you 3-(3/(cos^25a)) in partial fractions?
The solution
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3
3 - --------
25
cos (a)
$$3 - \frac{3}{\cos^{25}{\left(a \right)}}$$
3 - 3/cos(a)^25
Fraction decomposition
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3 - 3/cos(a)^25
$$3 - \frac{3}{\cos^{25}{\left(a \right)}}$$
3
3 - --------
25
cos (a)
Combinatorics
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/ 2 3 4 \ / 5 10 15 20 \
3*(-1 + cos(a))*\1 + cos (a) + cos (a) + cos (a) + cos(a)/*\1 + cos (a) + cos (a) + cos (a) + cos (a)/
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25
cos (a)
$$\frac{3 \left(\cos{\left(a \right)} - 1\right) \left(\cos^{4}{\left(a \right)} + \cos^{3}{\left(a \right)} + \cos^{2}{\left(a \right)} + \cos{\left(a \right)} + 1\right) \left(\cos^{20}{\left(a \right)} + \cos^{15}{\left(a \right)} + \cos^{10}{\left(a \right)} + \cos^{5}{\left(a \right)} + 1\right)}{\cos^{25}{\left(a \right)}}$$
3*(-1 + cos(a))*(1 + cos(a)^2 + cos(a)^3 + cos(a)^4 + cos(a))*(1 + cos(a)^5 + cos(a)^10 + cos(a)^15 + cos(a)^20)/cos(a)^25
Powers
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3
3 - ----------------
25
/ I*a -I*a\
|e e |
|---- + -----|
\ 2 2 /
$$3 - \frac{3}{\left(\frac{e^{i a}}{2} + \frac{e^{- i a}}{2}\right)^{25}}$$
3 - 3/(exp(i*a)/2 + exp(-i*a)/2)^25
Combining rational expressions
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/ 25 \
3*\-1 + cos (a)/
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25
cos (a)
$$\frac{3 \left(\cos^{25}{\left(a \right)} - 1\right)}{\cos^{25}{\left(a \right)}}$$
3*(-1 + cos(a)^25)/cos(a)^25