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

The general solution for sec^2(x)+tan(x)=0 is No Solution for x\in\mathbb{R}

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

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

No Solution for x \in R

Solution steps

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

Rewrite using trig identities

1 + tan (x) + tan^{2} (x) = 0

Solve by substitution

tan (x) = - \frac{1}{2} + i \frac{3}{2}, tan (x) = - \frac{1}{2} - i \frac{3}{2}

tan (x) = - \frac{1}{2} + i \frac{3}{2} :

No Solution

tan (x) = - \frac{1}{2} - i \frac{3}{2} :

No Solution

Combine all the solutions

No Solution for x \in R

sin (θ) cot^{2} (θ) - 3 sin (θ) = 0

- 6 sin (x) - 3 = 9

5 sin^{2} (x) + cos^{2} (x) = 2

cos (θ) = - \frac{3}{7}

tan (x) cos (x) = \frac{1}{2}

What is the general solution for sec^2(x)+tan(x)=0 ?
The general solution for sec^2(x)+tan(x)=0 is No Solution for x\in\mathbb{R}