What is the general solution for sec(x)+tan(x)=0 ?

The general solution for sec(x)+tan(x)=0 is No Solution for x\in\mathbb{R}

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sec(x)+tan(x)=0

sec (x) + tan (x) = 0

No Solution for x \in R

Solution steps

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{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

sin (x + \frac{π}{6}) - sin (x - \frac{7 π}{6}) = \frac{3}{2}

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

sin (2 x) + sin (x) = 0, 0 \leq x \leq 2 π

cos (2 t) = 0

sec (5 x) - 2 = 0

What is the general solution for sec(x)+tan(x)=0 ?
The general solution for sec(x)+tan(x)=0 is No Solution for x\in\mathbb{R}