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

The general solution for 2sin(x)tan(x)=tan(x) is x=pin,x= pi/6+2pin,x=(5pi)/6+2pin

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2sin(x)tan(x)=tan(x)

2 sin (x) tan (x) = tan (x)

x = πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

2 sin (x) tan (x) = tan (x)

Subtract

tan (x)

from both sides

2 sin (x) tan (x) - tan (x) = 0

Factor

2 sin (x) tan (x) - tan (x) : tan (x) (2 sin (x) - 1)

tan (x) (2 sin (x) - 1) = 0

Solving each part separately

tan (x) = 0 or 2 sin (x) - 1 = 0

tan (x) = 0 : x = πn

2 sin (x) - 1 = 0 : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Combine all the solutions

x = πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

4 csc (θ) + 5 = 0

cos (x) = - cos (x) + 2

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

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

10 cos^{2} (x) + 13 cos (x) + 4 = 0

What is the general solution for 2sin(x)tan(x)=tan(x) ?
The general solution for 2sin(x)tan(x)=tan(x) is x=pin,x= pi/6+2pin,x=(5pi)/6+2pin