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Oct
20
asked How to find the values of $m$ so $A \cap B = \emptyset$ and $A \cup B = (-3,+\infty)$?
Oct
20
revised How to transform the result of this integral into powers of $\sin\,x$?
added 18 characters in body
Oct
19
answered How to prove an expression by method of mathematical induction?
Oct
19
accepted How to prove an expression by method of mathematical induction?
Oct
19
comment How to prove an expression by method of mathematical induction?
I want to prove that step - by - step.
Oct
19
asked How to prove an expression by method of mathematical induction?
Oct
19
awarded  Critic
Oct
19
accepted How to receive the result of the integral $ \int\frac{1}{x}dx$ is $\ln|x|$?
Oct
19
asked How to receive the result of the integral $ \int\frac{1}{x}dx$ is $\ln|x|$?
Oct
18
comment How to transform the result of this integral into powers of $\sin\,x$?
I want the ansewr is $\ln\left|1 + \tan\dfrac{x}{2}\right|
Oct
18
comment How to transform the result of this integral into powers of $\sin\,x$?
In general, how to calculate the given integral? Please help me.
Oct
18
comment How to transform the result of this integral into powers of $\sin\,x$?
Your answer does not contain absolute value. I do not understand.
Oct
18
revised How to transform the result of this integral into powers of $\sin\,x$?
added 547 characters in body
Oct
17
comment How to transform the result of this integral into powers of $\sin\,x$?
With trigSet[Cos[x]^4 - Cos[x/2]^2, cos], I get \!(* TagBox[ RowBox[{"{", RowBox[{"1", "-", RowBox[{"9", " ", SuperscriptBox[ RowBox[{"Cos", "[", FractionBox["x", "2"], "]"}], "2"]}], "+", RowBox[{"24", " ", SuperscriptBox[ RowBox[{"Cos", "[", FractionBox["x", "2"], "]"}], "4"]}], "-", RowBox[{"32", " ", SuperscriptBox[ RowBox[{"Cos", "[", FractionBox["x", "2"], "]"}], "6"]}], "+", RowBox[{"16", " ", SuperscriptBox[ RowBox[{"Cos", "[", FractionBox["x", "2"], "]"}], "8"]}]}], "}"}], HoldForm])
Oct
17
accepted How to transform the result of this integral into powers of $\sin\,x$?
Oct
17
comment How to transform the result of this integral into powers of $\sin\,x$?
I am sorry when I ask the question.
Oct
17
revised How to transform the result of this integral into powers of $\sin\,x$?
added 1 characters in body
Oct
17
asked How to transform the result of this integral into powers of $\sin\,x$?
Oct
8
awarded  Enthusiast
Oct
6
comment Reduce an equation by putting a new variable
This method can be use to solve the system of the equations. For example \begin{equation*} \begin{cases} x^3 + y^3 = 2,\\ x^2 + y^2 -3xy=-1. \end{cases} \end{equation*} f[x_, y_] := x^3 + y^3 Eliminate[{f[x, y] == 2 // PowerExpand, x + y == S, x*y == P}, {x, y}] g[x_, y_] := x^2 + y^2 - 3*x*y Eliminate[{g[x, y] == -1 // PowerExpand, x + y == S, x*y == P}, {x, y}]