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

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

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tan(x)sec(x)=2tan(x)

tan (x) sec (x) = 2 tan (x)

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

Solution steps

tan (x) sec (x) = 2 tan (x)

Subtract

2 tan (x)

from both sides

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

Factor

tan (x) sec (x) - 2 tan (x) : tan (x) (sec (x) - 2)

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

Solving each part separately

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

tan (x) = 0 : x = πn

sec (x) - 2 = 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 (x) = \frac{5.1}{10.5}

tan (x) = 3, 0 \leq x < 2 π

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

sin (2 x) = 3 cos (x), 0 \leq x \leq 2 π

2 tan (A) - 1 = 0

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