What is the general solution for arccsc(2x)= pi/6 ?

The general solution for arccsc(2x)= pi/6 is x=1

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arccsc(2x)= pi/6

arccsc (2 x) = \frac{π}{6}

x = 1

Solution steps

arccsc (2 x) = \frac{π}{6}

Apply trig inverse properties

arccsc (2 x) = \frac{π}{6}

arccsc (x) = a \Rightarrow x = csc (a)

2 x = csc (\frac{π}{6})

csc (\frac{π}{6}) = 2

csc (\frac{π}{6})

Use the following trivial identity:

csc (\frac{π}{6}) = 2

csc (\frac{π}{6})

csc (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

= 2

= 2

2 x = 2

2 x = 2

Solve

2 x = 2 : x = 1

2 x = 2

Divide both sides by

2

2 x = 2

Divide both sides by

2

\frac{2 x}{2} = \frac{2}{2}

Simplify

x = 1

x = 1

x = 1

2 csc (θ) = 2 cot (θ) + 3 csc (θ)

sin (\frac{1}{2} x) = - 1

9 cos^{2} (x) tan (x) = 4 tan (x)

3 tan (x) - 3 = 0, 0 \leq x \leq 2 π

\frac{sin ( 57.2 2 ^{\circ} )}{31.5} = \frac{sin ( Q )}{24.4}

What is the general solution for arccsc(2x)= pi/6 ?
The general solution for arccsc(2x)= pi/6 is x=1