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

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

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solvefor x,arccsc(2x)= pi/6

solve for

x, 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

sin^{2} (x) + tan^{2} (x) = 1

cos (6 x) = sin (x - 1)

tan (θ) = \frac{72}{65}

cos (x) + cos (\frac{x}{2}) + 1 = 0

sin (x - 1) = sin (x)

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