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

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

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sec(x)=tan(x)

sec (x) = tan (x)

No Solution for x \in R

Solution steps

sec (x) = tan (x)

Subtract

tan (x)

from both sides

sec (x) - tan (x) = 0

Rewrite using trig identities

sec (x) - sec (x) sin (x) = 0

Factor

sec (x) - sec (x) sin (x) : - sec (x) (sin (x) - 1)

- sec (x) (sin (x) - 1) = 0

Solving each part separately

sec (x) = 0 or sin (x) - 1 = 0

sec (x) = 0 :

No Solution

sin (x) - 1 = 0 : x = \frac{π}{2} + 2 πn

Combine all the solutions

x = \frac{π}{2} + 2 πn

Since the equation is undefined for:

\frac{π}{2} + 2 πn

No Solution for x \in R

sin^{4} (x) = sin^{4} (x) sec (x)

sin (10 x) = 0

tan (\frac{x}{2}) + 6 = 0

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

cos (x) + sin (x) = 2

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