What is the general solution for 2sec^2(x)+5sec(x)+2=0 ?

The general solution for 2sec^2(x)+5sec(x)+2=0 is x=(2pi)/3+2pin,x=(4pi)/3+2pin

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2sec^2(x)+5sec(x)+2=0

2 sec^{2} (x) + 5 sec (x) + 2 = 0

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

Solution steps

2 sec^{2} (x) + 5 sec (x) + 2 = 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

sin^{2} (θ) = 8 (cos (- θ) + 1)

tan (x) = \frac{7.1}{5}

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

sin (2 θ) = - \frac{1}{2}, θ \geq 0

tan (x) = \frac{1}{3}, 0 \leq x \leq 2 π

What is the general solution for 2sec^2(x)+5sec(x)+2=0 ?
The general solution for 2sec^2(x)+5sec(x)+2=0 is x=(2pi)/3+2pin,x=(4pi)/3+2pin