What is the general solution for cos(8t)cos(5t)=-sin(8t)sin(5t) ?

The general solution for cos(8t)cos(5t)=-sin(8t)sin(5t) is t= pi/6+(2pin)/3 ,t= pi/2+(2pin)/3

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cos(8t)cos(5t)=-sin(8t)sin(5t)

cos (8 t) cos (5 t) = - sin (8 t) sin (5 t)

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

Solution steps

cos (8 t) cos (5 t) = - sin (8 t) sin (5 t)

Subtract

- sin (8 t) sin (5 t)

from both sides

cos (8 t) cos (5 t) + sin (8 t) sin (5 t) = 0

Rewrite using trig identities

cos (8 t - 5 t) = 0

General solutions for

cos (8 t - 5 t) = 0

8 t - 5 t = \frac{π}{2} + 2 πn, 8 t - 5 t = \frac{3 π}{2} + 2 πn

Solve

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

Solve

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

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

2 cos (θ) - 3 = - 5, 0 \leq θ < 2 π

2 tan (x) + 1 = 0

2 cos (3 x) + cos (2 x) + 1 = 0, 0 \leq x \leq 2 π

tan^{2} (x) = 3

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

What is the general solution for cos(8t)cos(5t)=-sin(8t)sin(5t) ?
The general solution for cos(8t)cos(5t)=-sin(8t)sin(5t) is t= pi/6+(2pin)/3 ,t= pi/2+(2pin)/3