What is the general solution for tan(x)csc(x)-2tan(x)=0 ?

The general solution for tan(x)csc(x)-2tan(x)=0 is x= pi/6+2pin,x=(5pi)/6+2pin

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

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

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

Solution steps

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

Factor

tan (x) csc (x) - 2 tan (x) : tan (x) (csc (x) - 2)

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

Solving each part separately

tan (x) = 0 or csc (x) - 2 = 0

tan (x) = 0 : x = πn

csc (x) - 2 = 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

Since the equation is undefined for:

πn

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

1 - 2 sin (θ) = 0

cos (2 θ) + 3 cos (θ) = 4

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

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

sin (x) = - \frac{1}{6}

What is the general solution for tan(x)csc(x)-2tan(x)=0 ?
The general solution for tan(x)csc(x)-2tan(x)=0 is x= pi/6+2pin,x=(5pi)/6+2pin