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

The general solution for 2tan^2(x)+3sec(x)=0 is x=(2pi)/3+2pin,x=(4pi)/3+2pin

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

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

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

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

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

No Solution

sec (x) = - 2 : x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Combine all the solutions

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

tan (x) = - \frac{3}{4}

tan (x) = - \frac{3}{2}

cos (2 θ) + 4 sin^{2} (θ) = 2

- 4 cos (4 x) = 0

4 csc^{2} (θ) - 25 = 0

What is the general solution for 2tan^2(x)+3sec(x)=0 ?
The general solution for 2tan^2(x)+3sec(x)=0 is x=(2pi)/3+2pin,x=(4pi)/3+2pin