English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tan(2arccos(1/4))

Solución

tan (2 arccos (\frac{1}{4}))

- \frac{15}{7}

Notación decimal

- 0.55328 \dots

Pasos de solución

tan (2 arccos (\frac{1}{4}))

Re-escribir usando identidades trigonométricas:

\frac{2 tan ( arccos ( \frac{1}{4} ) )}{1 - tan ^{2} ( arccos ( \frac{1}{4} ) )}

tan (2 arccos (\frac{1}{4}))

Utilizar la identidad trigonométrica del ángulo doble:

tan (2 x) = \frac{2 tan ( x )}{1 - tan ^{2} ( x )}

= \frac{2 tan ( arccos ( \frac{1}{4} ) )}{1 - tan ^{2} ( arccos ( \frac{1}{4} ) )}

= \frac{2 tan ( arccos ( \frac{1}{4} ) )}{1 - tan ^{2} ( arccos ( \frac{1}{4} ) )}

Re-escribir usando identidades trigonométricas:

tan (arccos (\frac{1}{4})) = 15

tan (arccos (\frac{1}{4}))

Re-escribir usando identidades trigonométricas:

tan (arccos (\frac{1}{4})) = \frac{1 - ( \frac{1}{4} ) ^{2}}{( \frac{1}{4} )}

Usar la siguiente identidad:

tan (arccos (x)) = \frac{1 - x ^{2}}{x}

= \frac{1 - ( \frac{1}{4} ) ^{2}}{( \frac{1}{4} )}

= \frac{1 - ( \frac{1}{4} ) ^{2}}{\frac{1}{4}}

Simplificar

= 15

= \frac{2 15}{1 - ( 15 ) ^{2}}

Simplificar

\frac{2 15}{1 - ( 15 ) ^{2}} : - \frac{15}{7}

\frac{2 15}{1 - ( 15 ) ^{2}}

(15)^{2} = 15

(15)^{2}

Aplicar las leyes de los exponentes:

a = a^{\frac{1}{2}}

= (1 5^{\frac{1}{2}})^{2}

Aplicar las leyes de los exponentes:

(a^{b})^{c} = a^{b c}

= 1 5^{\frac{1}{2} \cdot 2}

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

Multiplicar fracciones:

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

= \frac{1 \cdot 2}{2}

Eliminar los terminos comunes:

2

= 1

= 15

= \frac{2 15}{1 - 15}

Restar:

1 - 15 = - 14

= \frac{2 15}{- 14}

Aplicar las propiedades de las fracciones:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{2 15}{14}

Eliminar los terminos comunes:

2

= - \frac{15}{7}

= - \frac{15}{7}

\frac{sin ( 3 0 ^{\circ} ) + cos ( 3 0 ^{\circ} )}{tan ( 3 0 ^{\circ} )}

4 cos (3 0^{\circ}) + 6 sin (4 5^{\circ})

tan^{2} (\frac{5 π}{4})

5000 cos (3 0^{\circ})

sin (\frac{7}{12 \cdot π}) - cos (\frac{π}{12})