What is the value of -cot(pi/6)csc(pi/6) ?

The value of -cot(pi/6)csc(pi/6) is -sqrt(3)*2

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-cot(pi/6)csc(pi/6)

- cot (\frac{π}{6}) csc (\frac{π}{6})

- 3 \cdot 2

Decimal Notation

- 3.46410 \dots

Solution steps

- cot (\frac{π}{6}) csc (\frac{π}{6})

Use the following trivial identity:

cot (\frac{π}{6}) = 3

cot (\frac{π}{6})

cot (x)

periodicity table with

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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

= 3

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

= - 3 \cdot 2

tan (arctan (\frac{4}{3}) - arctan (\frac{1}{7}))

\frac{1}{2} sin (2 (\frac{π}{2}))

arcsin (\frac{1.5}{2.6})

arccos (22)

arccos (\frac{- 2}{3})

What is the value of -cot(pi/6)csc(pi/6) ?
The value of -cot(pi/6)csc(pi/6) is -sqrt(3)*2