sin(x+20)=cos(x-50)

Solución

sin (x + 2 0^{\circ}) = cos (x - 5 0^{\circ})

x = - 36 0^{\circ} n + 6 0^{\circ}, x = - 12 0^{\circ} - 36 0^{\circ} n

Pasos de solución

sin (x + 2 0^{\circ}) = cos (x - 5 0^{\circ})

Restar

cos (x - 5 0^{\circ})

de ambos lados

sin (x + 2 0^{\circ}) - cos (x - 5 0^{\circ}) = 0

Simplificar

sin (x + 2 0^{\circ}) - cos (x - 5 0^{\circ}) : sin (\frac{9 x + 18 0 ^{\circ}}{9}) - cos (\frac{18 x - 90 0 ^{\circ}}{18})

sin (\frac{9 x + 18 0 ^{\circ}}{9}) - cos (\frac{18 x - 90 0 ^{\circ}}{18}) = 0

Re-escribir usando identidades trigonométricas

- 2 sin (1 0^{\circ}) sin (\frac{- 3 x + 18 0 ^{\circ}}{3}) = 0

Dividir ambos lados entre

- 2 sin (1 0^{\circ})

sin (\frac{- 3 x + 18 0 ^{\circ}}{3}) = 0

Soluciones generales para

sin (\frac{- 3 x + 18 0 ^{\circ}}{3}) = 0

\frac{- 3 x + 18 0 ^{\circ}}{3} = 0 + 36 0^{\circ} n, \frac{- 3 x + 18 0 ^{\circ}}{3} = 18 0^{\circ} + 36 0^{\circ} n

Resolver

\frac{- 3 x + 18 0 ^{\circ}}{3} = 0 + 36 0^{\circ} n : x = - 36 0^{\circ} n + 6 0^{\circ}

Resolver

\frac{- 3 x + 18 0 ^{\circ}}{3} = 18 0^{\circ} + 36 0^{\circ} n : x = - 12 0^{\circ} - 36 0^{\circ} n

x = - 36 0^{\circ} n + 6 0^{\circ}, x = - 12 0^{\circ} - 36 0^{\circ} n

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

sin (2 x) = \frac{( 7 m - 9 )}{9}

A = 2 sin (3 0^{\circ} + x) - cos (x)

tan (θ) = \frac{1058}{1000}

sin (x) = \frac{1}{4}, sin (2 x)