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

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

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sec(θ)+tan(θ)=0

sec (θ) + tan (θ) = 0

No Solution for θ \in R

Solution steps

sec (θ) + tan (θ) = 0

Rewrite using trig identities

sec (θ) + sec (θ) sin (θ) = 0

Factor

sec (θ) + sec (θ) sin (θ) : sec (θ) (sin (θ) + 1)

sec (θ) (sin (θ) + 1) = 0

Solving each part separately

sec (θ) = 0 or sin (θ) + 1 = 0

sec (θ) = 0 :

No Solution

sin (θ) + 1 = 0 : θ = \frac{3 π}{2} + 2 πn

Combine all the solutions

θ = \frac{3 π}{2} + 2 πn

Since the equation is undefined for:

\frac{3 π}{2} + 2 πn

No Solution for θ \in R

sin (θ) = \frac{3.5}{5}

sec (a) = \frac{41}{12}, 2 π < a < \frac{5 π}{2}, sin (\frac{a}{2})

sin (2 x) = 0.3

sin (2 x) = 0.6

- 2 cos (t) = 0

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