What is the general solution for csc(θ)=-3/(sqrt(5)),tan(2θ) ?

The general solution for csc(θ)=-3/(sqrt(5)),tan(2θ) is No Solution for θ\in\mathbb{R}

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csc(θ)=-3/(sqrt(5)),tan(2θ)

csc (θ) = - \frac{3}{5}, tan (2 θ)

No Solution for θ \in R

Solution steps

csc (θ) = - \frac{3}{5}, tan (2 θ)

Simplify

- \frac{3}{5} : - \frac{3 5}{5}

- \frac{3}{5}

Multiply by the conjugate

\frac{5}{5}

= - \frac{3 5}{5 5}

55 = 5

55

Apply radical rule:

a a = a

55 = 5

= 5

= - \frac{3 5}{5}

csc (θ) = - \frac{3 5}{5}

Apply trig inverse properties

csc (θ) = - \frac{3 5}{5}

General solutions for

csc (θ) = - \frac{3 5}{5}

csc (x) = - a \Rightarrow x = arccsc (- a) + 2 πn, x = π + arccsc (a) + 2 πn

θ = arccsc (- \frac{3 5}{5}) + 2 πn, θ = π + arccsc (\frac{3 5}{5}) + 2 πn

θ = arccsc (- \frac{3 5}{5}) + 2 πn, θ = π + arccsc (\frac{3 5}{5}) + 2 πn

Solutions for the range

tan (2 θ)

No Solution for θ \in R

1 - sin (x) = 0

x, sin (x) = e

x, sin (x) = 3

3 cos (2 θ) + 5 cos (θ) + 2 = 0

32 sin (θ) - 3 = 0

What is the general solution for csc(θ)=-3/(sqrt(5)),tan(2θ) ?
The general solution for csc(θ)=-3/(sqrt(5)),tan(2θ) is No Solution for θ\in\mathbb{R}