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sin(2arccos((sqrt(2))/2))

Solución

sin (2 arccos (\frac{2}{2}))

1

Pasos de solución

sin (2 arccos (\frac{2}{2}))

Re-escribir usando identidades trigonométricas:

2 sin (arccos (\frac{2}{2})) cos (arccos (\frac{2}{2}))

sin (2 arccos (\frac{2}{2}))

Utilizar la identidad trigonométrica del ángulo doble:

sin (2 x) = 2 sin (x) cos (x)

= 2 sin (arccos (\frac{2}{2})) cos (arccos (\frac{2}{2}))

= 2 sin (arccos (\frac{2}{2})) cos (arccos (\frac{2}{2}))

Re-escribir usando identidades trigonométricas:

sin (arccos (\frac{2}{2})) = \frac{1}{2}

sin (arccos (\frac{2}{2}))

Re-escribir usando identidades trigonométricas:

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

Usar la siguiente identidad:

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

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

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

Simplificar

= \frac{1}{2}

Re-escribir usando identidades trigonométricas:

cos (arccos (\frac{2}{2})) = \frac{2}{2}

Usar la siguiente identidad:

cos (arccos (x)) = x

= \frac{2}{2}

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

Simplificar

2 \frac{1}{2} \frac{2}{2} : 1

2 \frac{1}{2} \frac{2}{2}

Multiplicar fracciones:

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

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

Eliminar los terminos comunes:

2

= 2 \frac{1}{2}

Aplicar las leyes de los exponentes:

a b = a \cdot b

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

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

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

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

Aplicar la regla

1 = 1

= 1

= 1

arccos (\frac{17}{28})

4 sec^{2} (1 8^{\circ}) - 4 tan^{2} (1 8^{\circ})

3 sin (\frac{π}{4}) + 3 cos (\frac{π}{4})

tan (\frac{- π}{2})

2 cos (\frac{π}{6}) + sin (2 (\frac{π}{6}))