Question

Find the solutions to the following equation on the interval (-inf, +inf). Round your answer to the nearest ten thousandth. Enter answers in increasing order.

5) sqrt3 sec theta + sec theta cot theta = 0

Answer 1

sqrt3 sec theta + sec theta cot theta = 0

Do you mean

√(3secθ+secθcotθ)=0?

Answer 2

I read it as
√3 secθ+secθcotθ=0
then:
secθ(√3 + cotθ) = 0

secθ = 0 <------ no solution

or

cotθ = -1/√3
tanθ = -1/√3
θ = 150° or 330° OR θ = 5π/6 or 11π/6 radians

looks good at Wolfram:
https://www.wolframalpha.com/input/?i=graph+y+%3D+%E2%88%9A3+sec%CE%B8%2Bsec%CE%B8cot%CE%B8


I will let you state the general solution since the domain is the set of all real θ's