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

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

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tan(x)=-sec(x)

tan (x) = - sec (x)

No Solution for x \in R

Solution steps

tan (x) = - sec (x)

Subtract

- sec (x)

from both sides

tan (x) + sec (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{3 π}{2} + 2 πn

Combine all the solutions

x = \frac{3 π}{2} + 2 πn

Since the equation is undefined for:

\frac{3 π}{2} + 2 πn

No Solution for x \in R

3 tan^{4} (θ) + 1 = \frac{2}{tan ^{2} ( θ )}

cos^{2} (s) = \frac{3}{4}

tan (\frac{θ}{2} + \frac{π}{4}) = 1, 0 \leq θ \leq 2 π

sin (x + \frac{π}{6}) + sin (x - \frac{π}{6}) = \frac{3}{2}

c, s = \frac{sin ^{2} ( c )}{2}

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