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

The general solution for tan(x)=2cos(x)tan(x) is x=pin,x= pi/3+2pin,x=(5pi)/3+2pin

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tan(x)=2cos(x)tan(x)

tan (x) = 2 cos (x) tan (x)

x = πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

tan (x) = 2 cos (x) tan (x)

Subtract

2 cos (x) tan (x)

from both sides

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

Factor

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

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

Solving each part separately

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

tan (x) = 0 : x = πn

2 cos (x) - 1 = 0 : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

x = πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

tan (θ) = 2.6

2 sin^{2} (x) = 1 + cos (x)

sin (θ) = \frac{8}{17}

cos^{2} (x) - 3 sin (x) = 3

7 sin (x) cos (x) = 8 cos (x)

What is the general solution for tan(x)=2cos(x)tan(x) ?
The general solution for tan(x)=2cos(x)tan(x) is x=pin,x= pi/3+2pin,x=(5pi)/3+2pin