What is the general solution for 1+sec^2(x)=tan(x) ?

The general solution for 1+sec^2(x)=tan(x) is No Solution for x\in\mathbb{R}

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

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

No Solution for x \in R

Solution steps

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

Subtract

tan (x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

tan (x) = \frac{1}{2} + i \frac{7}{2}, tan (x) = \frac{1}{2} - i \frac{7}{2}

tan (x) = \frac{1}{2} + i \frac{7}{2} :

No Solution

tan (x) = \frac{1}{2} - i \frac{7}{2} :

No Solution

Combine all the solutions

No Solution for x \in R

sin (θ) = 0.9903

tan (θ) = \frac{17}{7}

θ, cos (θ) = \frac{6}{85}

\frac{sin ( 8 0 ^{\circ} )}{5} = \frac{sin ( x )}{4}, x \cdot \frac{180}{π} = y

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

What is the general solution for 1+sec^2(x)=tan(x) ?
The general solution for 1+sec^2(x)=tan(x) is No Solution for x\in\mathbb{R}