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

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

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sec^2(x)=tan(x)

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

No Solution for x \in R

Solution steps

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

Subtract

tan (x)

from both sides

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

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

x, θ = arctan (\frac{y}{x})

cos (x) tan (x) = 10 tan (x)

cos (2 x) = \frac{3}{5}

- 4 cos (2 x) = 0

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