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

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

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((sec(x))/(cos(x)))^2=tan^2(x)

(\frac{sec ( x )}{cos ( x )})^{2} = tan^{2} (x)

No Solution for x \in R

Solution steps

(\frac{sec ( x )}{cos ( x )})^{2} = tan^{2} (x)

Subtract

tan^{2} (x)

from both sides

\frac{sec ^{2} ( x )}{cos ^{2} ( x )} - tan^{2} (x) = 0

Simplify

\frac{sec ^{2} ( x )}{cos ^{2} ( x )} - tan^{2} (x) : \frac{sec ^{2} ( x ) - tan ^{2} ( x ) cos ^{2} ( x )}{cos ^{2} ( x )}

\frac{sec ^{2} ( x ) - tan ^{2} ( x ) cos ^{2} ( x )}{cos ^{2} ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

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

Factor

sec^{2} (x) - tan^{2} (x) cos^{2} (x) : (sec (x) + tan (x) cos (x)) (sec (x) - tan (x) cos (x))

(sec (x) + tan (x) cos (x)) (sec (x) - tan (x) cos (x)) = 0

Solving each part separately

sec (x) + tan (x) cos (x) = 0 or sec (x) - tan (x) cos (x) = 0

sec (x) + tan (x) cos (x) = 0 :

No Solution

sec (x) - tan (x) cos (x) = 0 :

No Solution

Combine all the solutions

No Solution for x \in R

sin (\frac{x}{2}) - cos (\frac{x}{2}) = 0

2 sin^{2} (\frac{x}{3}) = 1, - π \leq, x \leq π

cos^{2} (x) + sin^{2} (x) = sin (x) + \frac{1}{2}

sin (A) = 0.53

tan (a) = 3, cos (a)

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