What is the general solution for 2tan^2(x)+4sec(x)+sec^2(x)=2 ?

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

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2tan^2(x)+4sec(x)+sec^2(x)=2

2 tan^{2} (x) + 4 sec (x) + sec^{2} (x) = 2

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

Solution steps

2 tan^{2} (x) + 4 sec (x) + sec^{2} (x) = 2

Subtract

2

from both sides

2 tan^{2} (x) + 4 sec (x) + sec^{2} (x) - 2 = 0

Rewrite using trig identities

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

Solve by substitution

sec (x) = \frac{2}{3}, sec (x) = - 2

sec (x) = \frac{2}{3} :

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

2 + cos (2 x) = - 3 cos (x), 0 \leq x \leq 2 π

sec (x + 1 0^{\circ}) = 5.759

cos (3 x + \frac{π}{4}) = \frac{3}{2}

- sin (4 x) = sin (8 x)

tan (θ) = \frac{3 3}{3}

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