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Popular >

cos(5t)cos(3t)= 1/2+sin(-5t)sin(3t)

Solución

cos (5 t) cos (3 t) = \frac{1}{2} + sin (- 5 t) sin (3 t)

Solución

t = \frac{π}{6} + πn, t = \frac{5 π}{6} + πn

+1

Pasos de solución

cos (5 t) cos (3 t) = \frac{1}{2} + sin (- 5 t) sin (3 t)

Re-escribir usando identidades trigonométricas

cos (5 t) cos (3 t) = \frac{1}{2} - sin (5 t) sin (3 t)

Restar

\frac{1}{2} - sin (5 t) sin (3 t)

de ambos lados

cos (5 t) cos (3 t) - \frac{1}{2} + sin (5 t) sin (3 t) = 0

Simplificar

cos (5 t) cos (3 t) - \frac{1}{2} + sin (5 t) sin (3 t) : \frac{2 cos ( 5 t ) cos ( 3 t ) - 1 + 2 sin ( 5 t ) sin ( 3 t )}{2}

\frac{2 cos ( 5 t ) cos ( 3 t ) - 1 + 2 sin ( 5 t ) sin ( 3 t )}{2} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

2 cos (5 t) cos (3 t) - 1 + 2 sin (5 t) sin (3 t) = 0

Re-escribir usando identidades trigonométricas

- 1 + 2 cos (2 t) = 0

Mover

1

al lado derecho

2 cos (2 t) = 1

Dividir ambos lados entre

2

cos (2 t) = \frac{1}{2}

Soluciones generales para

cos (2 t) = \frac{1}{2}

2 t = \frac{π}{3} + 2 πn, 2 t = \frac{5 π}{3} + 2 πn

Resolver

2 t = \frac{π}{3} + 2 πn : t = \frac{π}{6} + πn

Resolver

2 t = \frac{5 π}{3} + 2 πn : t = \frac{5 π}{6} + πn

t = \frac{π}{6} + πn, t = \frac{5 π}{6} + πn

Ejemplos populares

sin(3θ+72)=cos(48),0<= θ<= 360

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cot^2(y)+csc(y)-5=0

cot^{2} (y) + csc (y) - 5 = 0

2cos(θ)=1,0<= θ<2pi

2 cos (θ) = 1, 0 \leq θ < 2 π

cos^2(x)-tan(x)cos^2(x)=0

cos^{2} (x) - tan (x) cos^{2} (x) = 0

sqrt(3)tan(x)-1=0,0<= x<= 2pi

3 tan (x) - 1 = 0, 0 \leq x \leq 2 π