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

The general solution for tan^2(θ)+sec(θ)=-2 is No Solution for θ\in\mathbb{R}

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tan^2(θ)+sec(θ)=-2

tan^{2} (θ) + sec (θ) = - 2

No Solution for θ \in R

Solution steps

tan^{2} (θ) + sec (θ) = - 2

Subtract

- 2

from both sides

tan^{2} (θ) + sec (θ) + 2 = 0

Rewrite using trig identities

1 + sec (θ) + sec^{2} (θ) = 0

Solve by substitution

sec (θ) = - \frac{1}{2} + i \frac{3}{2}, sec (θ) = - \frac{1}{2} - i \frac{3}{2}

sec (θ) = - \frac{1}{2} + i \frac{3}{2} :

No Solution

sec (θ) = - \frac{1}{2} - i \frac{3}{2} :

No Solution

Combine all the solutions

No Solution for θ \in R

9 csc (x) = 63

sin (x) (cos (x) + 1) = 0

1 5^{2} = 1 2^{2} + 2 0^{2} - 2 \cdot 12 \cdot 20 \cdot cos (a)

5 sec (θ) - 2 sec^{2} (θ) = tan^{2} (θ) - 1

cos (2 x) + cos (x) = 0, (0, 2 π)

What is the general solution for tan^2(θ)+sec(θ)=-2 ?
The general solution for tan^2(θ)+sec(θ)=-2 is No Solution for θ\in\mathbb{R}