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

The general solution for 2tan^2(x)=-3+3sec(x) is x=2pin

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

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

x = 2 πn

Solution steps

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

Subtract

- 3 + 3 sec (x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

sec (x) = 1, sec (x) = \frac{1}{2}

sec (x) = 1 : x = 2 πn

sec (x) = \frac{1}{2} :

No Solution

Combine all the solutions

x = 2 πn

5 csc^{2} (\frac{θ}{2}) - 16 = 0

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

2 tan (x) = 3 csc (x)

sin (t) = \frac{120}{500} sin (11 0^{\circ})

tan (θ) + 1 = 3 + 3 cot (θ)

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