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

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

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

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

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

Solution steps

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

Subtract

3 sec (x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

sec (x) = 2, sec (x) = 1

sec (x) = 2 : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

sec (x) = 1 : x = 2 πn

Combine all the solutions

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

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

cot (θ) + tan (θ) = 2

3 cos^{2} (θ) - 1 = 0

sin (3 x - \frac{π}{6}) = - cos (3 x - \frac{π}{6})

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

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