What is the general solution for sin(x)= 1/(sqrt(6)),tan(x) ?

The general solution for sin(x)= 1/(sqrt(6)),tan(x) is No Solution for x\in\mathbb{R}

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sin(x)= 1/(sqrt(6)),tan(x)

sin (x) = \frac{1}{6}, tan (x)

No Solution for x \in R

Solution steps

sin (x) = \frac{1}{6}, tan (x)

Simplify

\frac{1}{6} : \frac{6}{6}

\frac{1}{6}

Multiply by the conjugate

\frac{6}{6}

= \frac{1 \cdot 6}{6 6}

1 \cdot 6 = 6

66 = 6

66

Apply radical rule:

a a = a

66 = 6

= 6

= \frac{6}{6}

sin (x) = \frac{6}{6}

Apply trig inverse properties

sin (x) = \frac{6}{6}

General solutions for

sin (x) = \frac{6}{6}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

x = arcsin (\frac{6}{6}) + 2 πn, x = π - arcsin (\frac{6}{6}) + 2 πn

x = arcsin (\frac{6}{6}) + 2 πn, x = π - arcsin (\frac{6}{6}) + 2 πn

Solutions for the range

tan (x)

No Solution for x \in R

2 sin^{2} (x) + sin (x) - 2 = 0

cos (θ) = \frac{25}{714}

cot^{2} (a) = 1

3 sec^{2} (x) - 4 = 0, 0 \leq x < 2 π

2 sec (θ) + 4 = 0

What is the general solution for sin(x)= 1/(sqrt(6)),tan(x) ?
The general solution for sin(x)= 1/(sqrt(6)),tan(x) is No Solution for x\in\mathbb{R}