(1+cos(4x))sin(4x)=cos^2(2x)

Solución

(1 + cos (4 x)) sin (4 x) = cos^{2} (2 x)

x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn, x = \frac{π}{24} + \frac{πn}{2}, x = \frac{5 π}{24} + \frac{πn}{2}

Pasos de solución

(1 + cos (4 x)) sin (4 x) = cos^{2} (2 x)

Restar

cos^{2} (2 x)

de ambos lados

sin (4 x) (1 + cos (4 x)) - cos^{2} (2 x) = 0

Re-escribir usando identidades trigonométricas

- cos^{2} (2 x) + 2 cos^{2} (2 x) sin (4 x) = 0

Factorizar

- cos^{2} (2 x) + 2 cos^{2} (2 x) sin (4 x) : cos^{2} (2 x) (2 sin (4 x) - 1)

cos^{2} (2 x) (2 sin (4 x) - 1) = 0

Resolver cada parte por separado

cos^{2} (2 x) = 0 or 2 sin (4 x) - 1 = 0

cos^{2} (2 x) = 0 : x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn

2 sin (4 x) - 1 = 0 : x = \frac{π}{24} + \frac{πn}{2}, x = \frac{5 π}{24} + \frac{πn}{2}

Combinar toda las soluciones

x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn, x = \frac{π}{24} + \frac{πn}{2}, x = \frac{5 π}{24} + \frac{πn}{2}

arcsin (\frac{3}{5}) + arccos (x) = π

cos (θ) = \frac{6}{7}

2 cos (2 θ) + 7 sin (θ) = 5

tan (x^{2}) = 1

cos (x) = \frac{5}{10}