What is the general solution for 4cos(x)sin(x)=-5sin(x) ?

The general solution for 4cos(x)sin(x)=-5sin(x) is x=2pin,x=pi+2pin

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4cos(x)sin(x)=-5sin(x)

4 cos (x) sin (x) = - 5 sin (x)

x = 2 πn, x = π + 2 πn

Solution steps

4 cos (x) sin (x) = - 5 sin (x)

Subtract

- 5 sin (x)

from both sides

4 cos (x) sin (x) + 5 sin (x) = 0

Factor

4 cos (x) sin (x) + 5 sin (x) : sin (x) (4 cos (x) + 5)

sin (x) (4 cos (x) + 5) = 0

Solving each part separately

sin (x) = 0 or 4 cos (x) + 5 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

4 cos (x) + 5 = 0 :

No Solution

Combine all the solutions

x = 2 πn, x = π + 2 πn

6 arccos (2 x) = 5 π

2 sin (x) + cot (x) - csc (x) = 0

cosh (x) = \frac{5}{3}

2 cos^{2} (x) - 3 sin (x) + 2 = 0

sin (θ) = 0.75

What is the general solution for 4cos(x)sin(x)=-5sin(x) ?
The general solution for 4cos(x)sin(x)=-5sin(x) is x=2pin,x=pi+2pin