What is the general solution for 2sin(4t)=2sin(4t)cos(4t) ?

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

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2sin(4t)=2sin(4t)cos(4t)

2 sin (4 t) = 2 sin (4 t) cos (4 t)

t = \frac{πn}{2}, t = \frac{π}{4} + \frac{πn}{2}

Solution steps

2 sin (4 t) = 2 sin (4 t) cos (4 t)

Subtract

2 sin (4 t) cos (4 t)

from both sides

2 sin (4 t) - 2 sin (4 t) cos (4 t) = 0

Factor

2 sin (4 t) - 2 sin (4 t) cos (4 t) : - 2 sin (4 t) (cos (4 t) - 1)

- 2 sin (4 t) (cos (4 t) - 1) = 0

Solving each part separately

sin (4 t) = 0 or cos (4 t) - 1 = 0

sin (4 t) = 0 : t = \frac{πn}{2}, t = \frac{π}{4} + \frac{πn}{2}

cos (4 t) - 1 = 0 : t = \frac{πn}{2}

Combine all the solutions

t = \frac{πn}{2}, t = \frac{π}{4} + \frac{πn}{2}

a^{1} sin (x) = 43.1253

52800 = \frac{( 1500 ) ^{2} sin ( x )}{32.2}

7 cos (3 x) = 2, 0 \leq x < 2 π

6 cos (2 x) = 3

arctan (\frac{x}{42}) = 57

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