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

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

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

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

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

Solution steps

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

Subtract

3 cos (x)

from both sides

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

Factor

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

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

Solving each part separately

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

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

2 sin (x) - 3 = 0 :

No Solution

Combine all the solutions

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

cos (x) sin (2 x) = 0

arcsin (x) - arccos (x) = arcsin (3 x - 2)

cos (a) = - 0.6

15 arcsin (x) = 5 π

2 sin^{2} (x) - sin (x) = 0, 0 \leq x < 2 π

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