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arccos(x)=arcsin(1/4)+arcsin(7/8)

Solución

arccos (x) = arcsin (\frac{1}{4}) + arcsin (\frac{7}{8})

Solución

x = \frac{1}{4}

Pasos de solución

arccos (x) = arcsin (\frac{1}{4}) + arcsin (\frac{7}{8})

Aplicar propiedades trigonométricas inversas

arccos (x) = arcsin (\frac{1}{4}) + arcsin (\frac{7}{8})

arccos (x) = a \Rightarrow x = cos (a)

x = cos (arcsin (\frac{1}{4}) + arcsin (\frac{7}{8}))

cos (arcsin (\frac{1}{4}) + arcsin (\frac{7}{8})) = \frac{1}{4}

cos (arcsin (\frac{1}{4}) + arcsin (\frac{7}{8}))

Re-escribir usando identidades trigonométricas:

cos (arcsin (\frac{1}{4})) cos (arcsin (\frac{7}{8})) - sin (arcsin (\frac{1}{4})) sin (arcsin (\frac{7}{8}))

cos (arcsin (\frac{1}{4}) + arcsin (\frac{7}{8}))

Utilizar la identidad de suma de ángulos:

cos (s + t) = cos (s) cos (t) - sin (s) sin (t)

= cos (arcsin (\frac{1}{4})) cos (arcsin (\frac{7}{8})) - sin (arcsin (\frac{1}{4})) sin (arcsin (\frac{7}{8}))

= cos (arcsin (\frac{1}{4})) cos (arcsin (\frac{7}{8})) - sin (arcsin (\frac{1}{4})) sin (arcsin (\frac{7}{8}))

Re-escribir usando identidades trigonométricas:

cos (arcsin (\frac{1}{4})) = \frac{15}{4}

cos (arcsin (\frac{1}{4}))

Re-escribir usando identidades trigonométricas:

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

Usar la siguiente identidad:

cos (arcsin (x)) = 1 - x^{2}

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

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

Simplificar

= \frac{15}{4}

Re-escribir usando identidades trigonométricas:

cos (arcsin (\frac{7}{8})) = \frac{15}{8}

cos (arcsin (\frac{7}{8}))

Re-escribir usando identidades trigonométricas:

cos (arcsin (\frac{7}{8})) = 1 - (\frac{7}{8})^{2}

Usar la siguiente identidad:

cos (arcsin (x)) = 1 - x^{2}

= 1 - (\frac{7}{8})^{2}

= 1 - (\frac{7}{8})^{2}

Simplificar

= \frac{15}{8}

Re-escribir usando identidades trigonométricas:

sin (arcsin (\frac{1}{4})) = \frac{1}{4}

Usar la siguiente identidad:

sin (arcsin (x)) = x

= \frac{1}{4}

Re-escribir usando identidades trigonométricas:

sin (arcsin (\frac{7}{8})) = \frac{7}{8}

Usar la siguiente identidad:

sin (arcsin (x)) = x

= \frac{7}{8}

= \frac{15}{4} \cdot \frac{15}{8} - \frac{1}{4} \cdot \frac{7}{8}

Simplificar

\frac{15}{4} \cdot \frac{15}{8} - \frac{1}{4} \cdot \frac{7}{8} : \frac{1}{4}

\frac{15}{4} \cdot \frac{15}{8} - \frac{1}{4} \cdot \frac{7}{8}

\frac{15}{4} \cdot \frac{15}{8} = \frac{15}{32}

\frac{15}{4} \cdot \frac{15}{8}

Multiplicar fracciones:

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

= \frac{15 15}{4 \cdot 8}

1515 = 15

1515

Aplicar las leyes de los exponentes:

a a = a

1515 = 15

= 15

= \frac{15}{4 \cdot 8}

Multiplicar los numeros:

4 \cdot 8 = 32

= \frac{15}{32}

\frac{1}{4} \cdot \frac{7}{8} = \frac{7}{32}

\frac{1}{4} \cdot \frac{7}{8}

Multiplicar fracciones:

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

= \frac{1 \cdot 7}{4 \cdot 8}

Multiplicar los numeros:

1 \cdot 7 = 7

= \frac{7}{4 \cdot 8}

Multiplicar los numeros:

4 \cdot 8 = 32

= \frac{7}{32}

= \frac{15}{32} - \frac{7}{32}

Aplicar la regla

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

= \frac{15 - 7}{32}

Restar:

15 - 7 = 8

= \frac{8}{32}

Eliminar los terminos comunes:

8

= \frac{1}{4}

= \frac{1}{4}

x = \frac{1}{4}

x = \frac{1}{4}

Ejemplos populares

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3 cot^{2} (2 t - \frac{3 π}{2}) = 1

3 cot (θ) - 2 = 0

sin (u) = \frac{5}{13}

0.8 = cos (x)

cos (x) = \frac{12}{20}