sin(x)+cos(x)= 2/3

Solución

sin (x) + cos (x) = \frac{2}{3}

x = 0.49088 \dots + 2 πn - \frac{π}{4}, x = π - 0.49088 \dots + 2 πn - \frac{π}{4}

Pasos de solución

sin (x) + cos (x) = \frac{2}{3}

Re-escribir usando identidades trigonométricas

2 sin (x + \frac{π}{4}) = \frac{2}{3}

Dividir ambos lados entre

2

sin (x + \frac{π}{4}) = \frac{2}{3}

Aplicar propiedades trigonométricas inversas

x + \frac{π}{4} = arcsin (\frac{2}{3}) + 2 πn, x + \frac{π}{4} = π - arcsin (\frac{2}{3}) + 2 πn

Resolver

x + \frac{π}{4} = arcsin (\frac{2}{3}) + 2 πn : x = arcsin (\frac{2}{3}) + 2 πn - \frac{π}{4}

Resolver

x + \frac{π}{4} = π - arcsin (\frac{2}{3}) + 2 πn : x = π - arcsin (\frac{2}{3}) + 2 πn - \frac{π}{4}

x = arcsin (\frac{2}{3}) + 2 πn - \frac{π}{4}, x = π - arcsin (\frac{2}{3}) + 2 πn - \frac{π}{4}

Mostrar soluciones en forma decimal

x = 0.49088 \dots + 2 πn - \frac{π}{4}, x = π - 0.49088 \dots + 2 πn - \frac{π}{4}

2 cos^{2} (2 θ) = 1 - cos (2 θ)

1 + tan^{2} (x) = 0

sin (x) = \frac{3}{8}

x, tan (x) + cot (x) = \frac{1}{f}

sec^{2} (x) - 1 + tan (x) - 3 tan (x) = 3