What is the general solution for sec^2(x)=sqrt(3)tan(x)+1 ?

The general solution for sec^2(x)=sqrt(3)tan(x)+1 is x= pi/3+pin,x=pin

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sec^2(x)=sqrt(3)tan(x)+1

sec^{2} (x) = 3 tan (x) + 1

x = \frac{π}{3} + πn, x = πn

Solution steps

sec^{2} (x) = 3 tan (x) + 1

Subtract

3 tan (x) + 1

from both sides

sec^{2} (x) - 3 tan (x) - 1 = 0

Rewrite using trig identities

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

Solve by substitution

tan (x) = 3, tan (x) = 0

tan (x) = 3 : x = \frac{π}{3} + πn

tan (x) = 0 : x = πn

Combine all the solutions

x = \frac{π}{3} + πn, x = πn

- 3 cos (2 θ) - sin (θ) - 6 = - 8

sin^{2} (x) + 1 = \frac{7}{2} cos^{2} (x)

cos (θ) sin (θ) - 2 cos (θ) = 0

y, x = tan^{2} (y)

tan (θ) = \frac{7}{3}

What is the general solution for sec^2(x)=sqrt(3)tan(x)+1 ?
The general solution for sec^2(x)=sqrt(3)tan(x)+1 is x= pi/3+pin,x=pin