What is the general solution for sec(x)=-(1/2)/(sqrt(3)) ?

The general solution for sec(x)=-(1/2)/(sqrt(3)) is No Solution for x\in\mathbb{R}

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sec(x)=-(1/2)/(sqrt(3))

sec (x) = - \frac{\frac{1}{2}}{3}

No Solution for x \in R

Solution steps

sec (x) = - \frac{\frac{1}{2}}{3}

Simplify

- \frac{\frac{1}{2}}{3} : - \frac{3}{6}

- \frac{\frac{1}{2}}{3}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= - \frac{1}{2 3}

Rationalize

- \frac{1}{2 3} : - \frac{3}{6}

- \frac{1}{2 3}

Multiply by the conjugate

\frac{3}{3}

= - \frac{1 \cdot 3}{2 3 3}

1 \cdot 3 = 3

233 = 6

233

Apply radical rule:

a a = a

33 = 3

= 2 \cdot 3

Multiply the numbers:

2 \cdot 3 = 6

= 6

= - \frac{3}{6}

= - \frac{3}{6}

sec (x) = - \frac{3}{6}

sec (x) \leq - 1 or sec (x) \geq 1

No Solution for x \in R

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What is the general solution for sec(x)=-(1/2)/(sqrt(3)) ?
The general solution for sec(x)=-(1/2)/(sqrt(3)) is No Solution for x\in\mathbb{R}