What is the value of -(2cot(pi/6)csc(pi/6))/((1-csc(pi/6))^2) ?

The value of -(2cot(pi/6)csc(pi/6))/((1-csc(pi/6))^2) is -4sqrt(3)

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-(2cot(pi/6)csc(pi/6))/((1-csc(pi/6))^2)

- \frac{2 cot ( \frac{π}{6} ) csc ( \frac{π}{6} )}{( 1 - csc ( \frac{π}{6} ) ) ^{2}}

- 43

Decimal Notation

- 6.92820 \dots

Solution steps

- \frac{2 cot ( \frac{π}{6} ) csc ( \frac{π}{6} )}{( 1 - csc ( \frac{π}{6} ) ) ^{2}}

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

= - \frac{2 3 \cdot 2}{( 1 - 2 ) ^{2}}

Simplify

- \frac{2 3 \cdot 2}{( 1 - 2 ) ^{2}} : - 43

- \frac{2 3 \cdot 2}{( 1 - 2 ) ^{2}}

Multiply the numbers:

2 \cdot 2 = 4

= - \frac{4 3}{( 1 - 2 ) ^{2}}

(1 - 2)^{2} = 1

(1 - 2)^{2}

Subtract the numbers:

1 - 2 = - 1

= (- 1)^{2}

Apply exponent rule:

(- a)^{n} = a^{n},

n

is even

(- 1)^{2} = 1^{2}

= 1^{2}

Apply rule

1^{a} = 1

= 1

= - \frac{4 3}{1}

Apply rule

\frac{a}{1} = a

= - 43

= - 43

cot (- 3 7^{\circ})

2 csc (4 5^{\circ})

csc (- \frac{17 π}{6})

arctan (2.75)

tan (\frac{38.71}{8.22})

What is the value of -(2cot(pi/6)csc(pi/6))/((1-csc(pi/6))^2) ?
The value of -(2cot(pi/6)csc(pi/6))/((1-csc(pi/6))^2) is -4sqrt(3)