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

The general solution for tan(x)sec(x)-2tan(x)=0 is x=pin,x= pi/3+2pin,x=(5pi)/3+2pin

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

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

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

Solution steps

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

- 9 cos^{2} (θ) + 9 = 17 sin (θ) - 8

θ, r = 2 cos (θ)

sin (2 x) = \frac{2 2}{3}

arccos (x) = \frac{15}{17}

4 tan^{2} (θ) - 9 = 0

What is the general solution for tan(x)sec(x)-2tan(x)=0 ?
The general solution for tan(x)sec(x)-2tan(x)=0 is x=pin,x= pi/3+2pin,x=(5pi)/3+2pin