What is the general solution for sin(4t)cos(t)=sin(t)cos(4t) ?

The general solution for sin(4t)cos(t)=sin(t)cos(4t) is t=(2pin)/3 ,t= pi/3+(2pin)/3

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sin(4t)cos(t)=sin(t)cos(4t)

sin (4 t) cos (t) = sin (t) cos (4 t)

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

Solution steps

sin (4 t) cos (t) = sin (t) cos (4 t)

Subtract

sin (t) cos (4 t)

from both sides

sin (4 t) cos (t) - sin (t) cos (4 t) = 0

Rewrite using trig identities

sin (4 t - t) = 0

General solutions for

sin (4 t - t) = 0

4 t - t = 0 + 2 πn, 4 t - t = π + 2 πn

Solve

4 t - t = 0 + 2 πn : t = \frac{2 πn}{3}

Solve

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

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

3 tan (3 x + \frac{π}{2}) + 1 = 0

- 2 sin (x) - 2 cos (x) = 0

7 sin (b) = 5 sin (7 0^{\circ})

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

cos (\frac{1}{2} x) = - 1, y = 2

What is the general solution for sin(4t)cos(t)=sin(t)cos(4t) ?
The general solution for sin(4t)cos(t)=sin(t)cos(4t) is t=(2pin)/3 ,t= pi/3+(2pin)/3