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¿Cómo vas a descomponer esta atan(1/(2*qrt(5))*7*(tag(x/2)+1)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src]
    /   7    /   /x\    \\
atan|-------*|tan|-| + 1||
    |    ___ \   \2/    /|
    \2*\/ 5              /
atan(725(tan(x2)+1))\operatorname{atan}{\left(\frac{7}{2 \sqrt{5}} \left(\tan{\left(\frac{x}{2} \right)} + 1\right) \right)}
atan((7/((2*sqrt(5))))*(tan(x/2) + 1))
Descomposición de una fracción [src]
atan(7*sqrt(5)/10 + 7*sqrt(5)*tan(x/2)/10)
atan(75tan(x2)10+7510)\operatorname{atan}{\left(\frac{7 \sqrt{5} \tan{\left(\frac{x}{2} \right)}}{10} + \frac{7 \sqrt{5}}{10} \right)}
    /              ___    /x\\
    |    ___   7*\/ 5 *tan|-||
    |7*\/ 5               \2/|
atan|------- + --------------|
    \   10           10      /
Simplificación general [src]
    /    ___ /       /x\\\
    |7*\/ 5 *|1 + tan|-|||
    |        \       \2//|
atan|--------------------|
    \         10         /
atan(75(tan(x2)+1)10)\operatorname{atan}{\left(\frac{7 \sqrt{5} \left(\tan{\left(\frac{x}{2} \right)} + 1\right)}{10} \right)}
atan(7*sqrt(5)*(1 + tan(x/2))/10)
Respuesta numérica [src]
atan((7/((2*sqrt(5))))*(tan(x/2) + 1))
atan((7/((2*sqrt(5))))*(tan(x/2) + 1))
Denominador común [src]
    /              ___    /x\\
    |    ___   7*\/ 5 *tan|-||
    |7*\/ 5               \2/|
atan|------- + --------------|
    \   10           10      /
atan(75tan(x2)10+7510)\operatorname{atan}{\left(\frac{7 \sqrt{5} \tan{\left(\frac{x}{2} \right)}}{10} + \frac{7 \sqrt{5}}{10} \right)}
atan(7*sqrt(5)/10 + 7*sqrt(5)*tan(x/2)/10)
Combinatoria [src]
    /              ___    /x\\
    |    ___   7*\/ 5 *tan|-||
    |7*\/ 5               \2/|
atan|------- + --------------|
    \   10           10      /
atan(75tan(x2)10+7510)\operatorname{atan}{\left(\frac{7 \sqrt{5} \tan{\left(\frac{x}{2} \right)}}{10} + \frac{7 \sqrt{5}}{10} \right)}
atan(7*sqrt(5)/10 + 7*sqrt(5)*tan(x/2)/10)
Denominador racional [src]
    /    ___ /       /x\\\
    |7*\/ 5 *|1 + tan|-|||
    |        \       \2//|
atan|--------------------|
    \         10         /
atan(75(tan(x2)+1)10)\operatorname{atan}{\left(\frac{7 \sqrt{5} \left(\tan{\left(\frac{x}{2} \right)} + 1\right)}{10} \right)}
atan(7*sqrt(5)*(1 + tan(x/2))/10)
Abrimos la expresión [src]
    /    ___ /   /x\    \\
    |7*\/ 5 *|tan|-| + 1||
    |        \   \2/    /|
atan|--------------------|
    \         10         /
atan(75(tan(x2)+1)10)\operatorname{atan}{\left(\frac{7 \sqrt{5} \left(\tan{\left(\frac{x}{2} \right)} + 1\right)}{10} \right)}
    /              ___    /x\\
    |    ___   7*\/ 5 *tan|-||
    |7*\/ 5               \2/|
atan|------- + --------------|
    \   10           10      /
atan(75tan(x2)10+7510)\operatorname{atan}{\left(\frac{7 \sqrt{5} \tan{\left(\frac{x}{2} \right)}}{10} + \frac{7 \sqrt{5}}{10} \right)}
atan(7*sqrt(5)/10 + 7*sqrt(5)*tan(x/2)/10)
Potencias [src]
    /      /          /x\\\
    |      |     7*tan|-|||
    |  ___ |7         \2/||
atan|\/ 5 *|-- + --------||
    \      \10      10   //
atan(5(7tan(x2)10+710))\operatorname{atan}{\left(\sqrt{5} \left(\frac{7 \tan{\left(\frac{x}{2} \right)}}{10} + \frac{7}{10}\right) \right)}
    /        /      /   I*x    -I*x \\\
    |        |      |   ---    -----|||
    |        |      |    2       2  |||
    |    ___ |    I*\- e    + e     /||
    |7*\/ 5 *|1 + -------------------||
    |        |        I*x    -I*x    ||
    |        |        ---    -----   ||
    |        |         2       2     ||
    |        \       e    + e        /|
atan|---------------------------------|
    \                10               /
atan(75(i(eix2+eix2)eix2+eix2+1)10)\operatorname{atan}{\left(\frac{7 \sqrt{5} \left(\frac{i \left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)}{e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}} + 1\right)}{10} \right)}
    /    ___ /       /x\\\
    |7*\/ 5 *|1 + tan|-|||
    |        \       \2//|
atan|--------------------|
    \         10         /
atan(75(tan(x2)+1)10)\operatorname{atan}{\left(\frac{7 \sqrt{5} \left(\tan{\left(\frac{x}{2} \right)} + 1\right)}{10} \right)}
atan(7*sqrt(5)*(1 + tan(x/2))/10)
Parte trigonométrica [src]
    /        /       /x\\\
    |        |    sin|-|||
    |    ___ |       \2/||
    |7*\/ 5 *|1 + ------||
    |        |       /x\||
    |        |    cos|-|||
    |        \       \2//|
atan|--------------------|
    \         10         /
atan(75(sin(x2)cos(x2)+1)10)\operatorname{atan}{\left(\frac{7 \sqrt{5} \left(\frac{\sin{\left(\frac{x}{2} \right)}}{\cos{\left(\frac{x}{2} \right)}} + 1\right)}{10} \right)}
    /    ___ /      1   \\
    |7*\/ 5 *|1 + ------||
    |        |       /x\||
    |        |    cot|-|||
    |        \       \2//|
atan|--------------------|
    \         10         /
atan(75(1+1cot(x2))10)\operatorname{atan}{\left(\frac{7 \sqrt{5} \left(1 + \frac{1}{\cot{\left(\frac{x}{2} \right)}}\right)}{10} \right)}
    /    ___ /       csc(x)           \\
    |7*\/ 5 *|1 - ----------- + csc(x)||
    |        |       /pi    \         ||
    |        |    csc|-- - x|         ||
    |        \       \2     /         /|
atan|----------------------------------|
    \                10                /
atan(75(csc(x)csc(x)csc(x+π2)+1)10)\operatorname{atan}{\left(\frac{7 \sqrt{5} \left(\csc{\left(x \right)} - \frac{\csc{\left(x \right)}}{\csc{\left(- x + \frac{\pi}{2} \right)}} + 1\right)}{10} \right)}
    /    ___ /      1        1   \\
    |7*\/ 5 *|1 + ------ - ------||
    |        \    sin(x)   tan(x)/|
atan|-----------------------------|
    \              10             /
atan(75(11tan(x)+1sin(x))10)\operatorname{atan}{\left(\frac{7 \sqrt{5} \left(1 - \frac{1}{\tan{\left(x \right)}} + \frac{1}{\sin{\left(x \right)}}\right)}{10} \right)}
    /        /       /x   pi\\\
    |        |    cos|- - --|||
    |    ___ |       \2   2 /||
    |7*\/ 5 *|1 + -----------||
    |        |          /x\  ||
    |        |       cos|-|  ||
    |        \          \2/  /|
atan|-------------------------|
    \            10           /
atan(75(1+cos(x2π2)cos(x2))10)\operatorname{atan}{\left(\frac{7 \sqrt{5} \left(1 + \frac{\cos{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\cos{\left(\frac{x}{2} \right)}}\right)}{10} \right)}
    /    ___ /      1            \\
    |7*\/ 5 *|1 - ------ + csc(x)||
    |        \    tan(x)         /|
atan|-----------------------------|
    \              10             /
atan(75(csc(x)+11tan(x))10)\operatorname{atan}{\left(\frac{7 \sqrt{5} \left(\csc{\left(x \right)} + 1 - \frac{1}{\tan{\left(x \right)}}\right)}{10} \right)}
    /    ___ /       /x\\\
    |7*\/ 5 *|1 + tan|-|||
    |        \       \2//|
atan|--------------------|
    \         10         /
atan(75(tan(x2)+1)10)\operatorname{atan}{\left(\frac{7 \sqrt{5} \left(\tan{\left(\frac{x}{2} \right)} + 1\right)}{10} \right)}
    /        /          /x\  \\
    |        |       sec|-|  ||
    |    ___ |          \2/  ||
    |7*\/ 5 *|1 + -----------||
    |        |       /x   pi\||
    |        |    sec|- - --|||
    |        \       \2   2 //|
atan|-------------------------|
    \            10           /
atan(75(sec(x2)sec(x2π2)+1)10)\operatorname{atan}{\left(\frac{7 \sqrt{5} \left(\frac{\sec{\left(\frac{x}{2} \right)}}{\sec{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + 1\right)}{10} \right)}
    /        /       /    pi\              \\
    |        |    sec|x - --|              ||
    |    ___ |       \    2 /      /    pi\||
    |7*\/ 5 *|1 - ----------- + sec|x - --|||
    |        \       sec(x)        \    2 //|
atan|---------------------------------------|
    \                   10                  /
atan(75(sec(xπ2)+1sec(xπ2)sec(x))10)\operatorname{atan}{\left(\frac{7 \sqrt{5} \left(\sec{\left(x - \frac{\pi}{2} \right)} + 1 - \frac{\sec{\left(x - \frac{\pi}{2} \right)}}{\sec{\left(x \right)}}\right)}{10} \right)}
    /        /       /x\\\
    |        |    sec|-|||
    |    ___ |       \2/||
    |7*\/ 5 *|1 + ------||
    |        |       /x\||
    |        |    csc|-|||
    |        \       \2//|
atan|--------------------|
    \         10         /
atan(75(1+sec(x2)csc(x2))10)\operatorname{atan}{\left(\frac{7 \sqrt{5} \left(1 + \frac{\sec{\left(\frac{x}{2} \right)}}{\csc{\left(\frac{x}{2} \right)}}\right)}{10} \right)}
    /        /         2/x\\\
    |        |    2*sin |-|||
    |    ___ |          \2/||
    |7*\/ 5 *|1 + ---------||
    |        \      sin(x) /|
atan|-----------------------|
    \           10          /
atan(75(2sin2(x2)sin(x)+1)10)\operatorname{atan}{\left(\frac{7 \sqrt{5} \left(\frac{2 \sin^{2}{\left(\frac{x}{2} \right)}}{\sin{\left(x \right)}} + 1\right)}{10} \right)}
    /    ___ /      1            \\
    |7*\/ 5 *|1 + ------ - cot(x)||
    |        \    sin(x)         /|
atan|-----------------------------|
    \              10             /
atan(75(cot(x)+1+1sin(x))10)\operatorname{atan}{\left(\frac{7 \sqrt{5} \left(- \cot{\left(x \right)} + 1 + \frac{1}{\sin{\left(x \right)}}\right)}{10} \right)}
    /        /       /pi   x\\\
    |        |    csc|-- - -|||
    |    ___ |       \2    2/||
    |7*\/ 5 *|1 + -----------||
    |        |          /x\  ||
    |        |       csc|-|  ||
    |        \          \2/  /|
atan|-------------------------|
    \            10           /
atan(75(1+csc(x2+π2)csc(x2))10)\operatorname{atan}{\left(\frac{7 \sqrt{5} \left(1 + \frac{\csc{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{\csc{\left(\frac{x}{2} \right)}}\right)}{10} \right)}
    /        /                    2/x\\\
    |        |             1 + tan |-|||
    |    ___ |      1              \2/||
    |7*\/ 5 *|1 - ------ + -----------||
    |        |    tan(x)          /x\ ||
    |        |               2*tan|-| ||
    |        \                    \2/ /|
atan|----------------------------------|
    \                10                /
atan(75(tan2(x2)+12tan(x2)+11tan(x))10)\operatorname{atan}{\left(\frac{7 \sqrt{5} \left(\frac{\tan^{2}{\left(\frac{x}{2} \right)} + 1}{2 \tan{\left(\frac{x}{2} \right)}} + 1 - \frac{1}{\tan{\left(x \right)}}\right)}{10} \right)}
    /    ___ /         1           cos(x)  \\
    |7*\/ 5 *|1 + ----------- - -----------||
    |        |       /    pi\      /    pi\||
    |        |    cos|x - --|   cos|x - --|||
    |        \       \    2 /      \    2 //|
atan|---------------------------------------|
    \                   10                  /
atan(75(cos(x)cos(xπ2)+1+1cos(xπ2))10)\operatorname{atan}{\left(\frac{7 \sqrt{5} \left(- \frac{\cos{\left(x \right)}}{\cos{\left(x - \frac{\pi}{2} \right)}} + 1 + \frac{1}{\cos{\left(x - \frac{\pi}{2} \right)}}\right)}{10} \right)}
    /    ___ /      1       sin(2*x)\\
    |7*\/ 5 *|1 + ------ - ---------||
    |        |    sin(x)        2   ||
    |        \             2*sin (x)/|
atan|--------------------------------|
    \               10               /
atan(75(1+1sin(x)sin(2x)2sin2(x))10)\operatorname{atan}{\left(\frac{7 \sqrt{5} \left(1 + \frac{1}{\sin{\left(x \right)}} - \frac{\sin{\left(2 x \right)}}{2 \sin^{2}{\left(x \right)}}\right)}{10} \right)}
    /        /                    2/x\\\
    |        |             1 + cot |-|||
    |    ___ |                     \2/||
    |7*\/ 5 *|1 - cot(x) + -----------||
    |        |                    /x\ ||
    |        |               2*cot|-| ||
    |        \                    \2/ /|
atan|----------------------------------|
    \                10                /
atan(75(cot2(x2)+12cot(x2)cot(x)+1)10)\operatorname{atan}{\left(\frac{7 \sqrt{5} \left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} + 1}{2 \cot{\left(\frac{x}{2} \right)}} - \cot{\left(x \right)} + 1\right)}{10} \right)}
atan(7*sqrt(5)*(1 - cot(x) + (1 + cot(x/2)^2)/(2*cot(x/2)))/10)
Unión de expresiones racionales [src]
    /    ___ /       /x\\\
    |7*\/ 5 *|1 + tan|-|||
    |        \       \2//|
atan|--------------------|
    \         10         /
atan(75(tan(x2)+1)10)\operatorname{atan}{\left(\frac{7 \sqrt{5} \left(\tan{\left(\frac{x}{2} \right)} + 1\right)}{10} \right)}
atan(7*sqrt(5)*(1 + tan(x/2))/10)