What is the general solution for 2cos(x)sin(x)-3sin(x)=0 ?

The general solution for 2cos(x)sin(x)-3sin(x)=0 is x=2pin,x=pi+2pin

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2cos(x)sin(x)-3sin(x)=0

2 cos (x) sin (x) - 3 sin (x) = 0

x = 2 πn, x = π + 2 πn

Solution steps

2 cos (x) sin (x) - 3 sin (x) = 0

Factor

2 cos (x) sin (x) - 3 sin (x) : sin (x) (2 cos (x) - 3)

sin (x) (2 cos (x) - 3) = 0

Solving each part separately

sin (x) = 0 or 2 cos (x) - 3 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

2 cos (x) - 3 = 0 :

No Solution

Combine all the solutions

x = 2 πn, x = π + 2 πn

tan^{2} (θ) - 3 tan (θ) = 0

x, tan (x) = 0

cos (θ) = - sin (- θ)

sin (x) - 3 cos (x) = 3

cot^{2} (x) - 2 csc (x) = - 1

What is the general solution for 2cos(x)sin(x)-3sin(x)=0 ?
The general solution for 2cos(x)sin(x)-3sin(x)=0 is x=2pin,x=pi+2pin