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

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

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

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

No Solution for x \in R

Solution steps

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

Subtract

\frac{sec ( x )}{cos ( x )}

from both sides

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

Simplify

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

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

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

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

Express with sin, cos

\frac{- 1 + cos ( x ) sin ( x )}{cos ( x )} = 0

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

- 1 + cos (x) sin (x) = 0

Rewrite using trig identities

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

Move

1

to the right side

\frac{sin ( 2 x )}{2} = 1

Multiply both sides by

2

sin (2 x) = 2

- 1 \leq sin (x) \leq 1

No Solution for x \in R

sin (x) = - 0.707

2 sin^{2} (x) + 5 sin (x) = 0

cos (2 x) - 7 cos (x) - 3 = 0

tan^{2} (4 5^{\circ} - \frac{x}{3}) = 0.58

- 20 csc (x) = 40

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