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arctan(x)+arctan(2)=arctan(7)

Solución

arctan (x) + arctan (2) = arctan (7)

x = \frac{1}{3}

Pasos de solución

arctan (x) + arctan (2) = arctan (7)

Mover

arctan (2)

al lado derecho

arctan (x) + arctan (2) = arctan (7)

Restar

arctan (2)

de ambos lados

arctan (x) + arctan (2) - arctan (2) = arctan (7) - arctan (2)

Simplificar

arctan (x) = arctan (7) - arctan (2)

arctan (x) = arctan (7) - arctan (2)

Aplicar propiedades trigonométricas inversas

arctan (x) = arctan (7) - arctan (2)

arctan (x) = a \Rightarrow x = tan (a)

x = tan (arctan (7) - arctan (2))

tan (arctan (7) - arctan (2)) = \frac{1}{3}

tan (arctan (7) - arctan (2))

Re-escribir usando identidades trigonométricas:

arctan (7) - arctan (2) = arctan (\frac{1}{3})

arctan (7) - arctan (2)

Utilizar la identidad suma-producto:

arctan (s) - arctan (t) = arctan (\frac{s - t}{1 + s t})

= arctan (\frac{7 - 2}{1 + 7 \cdot 2})

Simplificar:

\frac{7 - 2}{1 + 7 \cdot 2} = \frac{1}{3}

\frac{7 - 2}{1 + 7 \cdot 2}

Restar:

7 - 2 = 5

= \frac{5}{1 + 7 \cdot 2}

1 + 7 \cdot 2 = 15

1 + 7 \cdot 2

Multiplicar los numeros:

7 \cdot 2 = 14

= 1 + 14

Sumar:

1 + 14 = 15

= 15

= \frac{5}{15}

Eliminar los terminos comunes:

5

= \frac{1}{3}

= arctan (\frac{1}{3})

= tan (arctan (\frac{1}{3}))

Re-escribir usando identidades trigonométricas:

tan (arctan (\frac{1}{3})) = \frac{1}{3}

Usar la siguiente identidad:

tan (arctan (x)) = x

= \frac{1}{3}

= \frac{1}{3}

x = \frac{1}{3}

x = \frac{1}{3}

3 sec (x) - 1 = 2

sec (x) = 6

sin (θ) = \frac{8}{12}

y, \int x d x = csc^{2} (\frac{y}{2})

sec (x) + 2 = 0, - π \leq x \leq \frac{3 π}{2}