What is the general solution for cos(x)sin(x)=-2sin(x) ?

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

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

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

x = 2 πn, x = π + 2 πn

Solution steps

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

Subtract

- 2 sin (x)

from both sides

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

Factor

cos (x) sin (x) + 2 sin (x) : sin (x) (cos (x) + 2)

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

Solving each part separately

sin (x) = 0 or cos (x) + 2 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

cos (x) + 2 = 0 :

No Solution

Combine all the solutions

x = 2 πn, x = π + 2 πn

(csc (θ) - 2) (cot (θ) + 1) = 0

sin (x) = csc (x)

9 sin (x) tan (x) = 10 tan (x)

3 sin^{2} (θ) + 6 = 2 sin^{2} (θ) + 7

10 sin^{2} (4 x) = 5

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