What is the general solution for sqrt(3)sec^2(x)+2tan(x)-2sqrt(3)=0 ?

The general solution for sqrt(3)sec^2(x)+2tan(x)-2sqrt(3)=0 is x= pi/6+pin,x=(2pi)/3+pin

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sqrt(3)sec^2(x)+2tan(x)-2sqrt(3)=0

3 sec^{2} (x) + 2 tan (x) - 23 = 0

x = \frac{π}{6} + πn, x = \frac{2 π}{3} + πn

Solution steps

3 sec^{2} (x) + 2 tan (x) - 23 = 0

Rewrite using trig identities

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

Solve by substitution

tan (x) = \frac{3}{3}, tan (x) = - 3

tan (x) = \frac{3}{3} : x = \frac{π}{6} + πn

tan (x) = - 3 : x = \frac{2 π}{3} + πn

Combine all the solutions

x = \frac{π}{6} + πn, x = \frac{2 π}{3} + πn

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

4 cos^{2} (x) + 3 cos (x) = 1

sin (x) = 4 cos (x)

7 cos (x) = 0

sin (θ) = \frac{3 13}{13}, sec (θ)

What is the general solution for sqrt(3)sec^2(x)+2tan(x)-2sqrt(3)=0 ?
The general solution for sqrt(3)sec^2(x)+2tan(x)-2sqrt(3)=0 is x= pi/6+pin,x=(2pi)/3+pin