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cos(2arcsin((sqrt(2))/2))

Solución

cos (2 arcsin (\frac{2}{2}))

0

Pasos de solución

cos (2 arcsin (\frac{2}{2}))

Re-escribir usando identidades trigonométricas:

1 - 2 sin^{2} (arcsin (\frac{2}{2}))

cos (2 arcsin (\frac{2}{2}))

Utilizar la identidad trigonométrica del ángulo doble:

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

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

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

Re-escribir usando identidades trigonométricas:

sin (arcsin (\frac{2}{2})) = \frac{2}{2}

Usar la siguiente identidad:

sin (arcsin (x)) = x

= \frac{2}{2}

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

Simplificar

1 - 2 (\frac{2}{2})^{2} : 0

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

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

2 (\frac{2}{2})^{2}

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

(\frac{2}{2})^{2}

Aplicar las leyes de los exponentes:

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

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

(2)^{2} : 2

Aplicar las leyes de los exponentes:

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

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

Aplicar las leyes de los exponentes:

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

= 2^{\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

= 2

= \frac{2}{2 ^{2}}

Eliminar los terminos comunes:

2

= \frac{1}{2}

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

Multiplicar fracciones:

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

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

Eliminar los terminos comunes:

2

= 1

= 1 - 1

Restar:

1 - 1 = 0

= 0

= 0

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