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Popular >

tan(2x)=(80}{\frac{30+20)/2}

Solución

tan (2 x) = \frac{80}{\frac{30 + 20}{2}}

x = \frac{1.26791 \dots}{2} + \frac{πn}{2}

radianes

x = \frac{1.26791 \dots}{2} + \frac{π}{2} n

Pasos de solución

tan (2 x) = \frac{80}{\frac{30 + 20}{2}}

Simplificar

\frac{80}{\frac{30 + 20}{2}} : \frac{16}{5}

\frac{80}{\frac{30 + 20}{2}}

Sumar:

30 + 20 = 50

= \frac{80}{\frac{50}{2}}

Aplicar las propiedades de las fracciones:

\frac{a}{\frac{b}{c}} = \frac{a \cdot c}{b}

= \frac{80 \cdot 2}{50}

Multiplicar los numeros:

80 \cdot 2 = 160

= \frac{160}{50}

Eliminar los terminos comunes:

10

= \frac{16}{5}

Aplicar propiedades trigonométricas inversas

tan (2 x) = \frac{16}{5}

Soluciones generales para

tan (2 x) = \frac{16}{5}

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

2 x = arctan (\frac{16}{5}) + πn

2 x = arctan (\frac{16}{5}) + πn

Resolver

2 x = arctan (\frac{16}{5}) + πn : x = \frac{arctan ( \frac{16}{5} )}{2} + \frac{πn}{2}

2 x = arctan (\frac{16}{5}) + πn

Dividir ambos lados entre

2

2 x = arctan (\frac{16}{5}) + πn

Dividir ambos lados entre

2

\frac{2 x}{2} = \frac{arctan ( \frac{16}{5} )}{2} + \frac{πn}{2}

Simplificar

x = \frac{arctan ( \frac{16}{5} )}{2} + \frac{πn}{2}

x = \frac{arctan ( \frac{16}{5} )}{2} + \frac{πn}{2}

x = \frac{arctan ( \frac{16}{5} )}{2} + \frac{πn}{2}

Mostrar soluciones en forma decimal

x = \frac{1.26791 \dots}{2} + \frac{πn}{2}

tan^{2} (x) + 1 = 4 tan (x)

(sin (x) - 1) (cos (x) - \frac{1}{2}) = 0

2 sin^{4} (x) = 4 - 7 cos^{2} (x)

4 cos^{2} (A) - 1 = 0

sin (\frac{75 π}{11}) = sin (\frac{x π}{11})