What is the value of 4+cot(pi/3)-2csc(pi/3) ?

The value of 4+cot(pi/3)-2csc(pi/3) is 4-sqrt(3)

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4+cot(pi/3)-2csc(pi/3)

4 + cot (\frac{π}{3}) - 2 csc (\frac{π}{3})

4 - 3

Decimal Notation

2.26794 \dots

Solution steps

4 + cot (\frac{π}{3}) - 2 csc (\frac{π}{3})

Use the following trivial identity:

cot (\frac{π}{3}) = \frac{3}{3}

cot (\frac{π}{3})

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

= \frac{3}{3}

Use the following trivial identity:

csc (\frac{π}{3}) = \frac{2 3}{3}

csc (\frac{π}{3})

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

= \frac{2 3}{3}

= 4 + \frac{3}{3} - 2 \cdot \frac{2 3}{3}

Simplify

4 + \frac{3}{3} - 2 \cdot \frac{2 3}{3} : 4 - 3

4 + \frac{3}{3} - 2 \cdot \frac{2 3}{3}

2 \cdot \frac{2 3}{3} = \frac{4 3}{3}

2 \cdot \frac{2 3}{3}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 3 \cdot 2}{3}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{4 3}{3}

= 4 + \frac{3}{3} - \frac{4 3}{3}

Combine the fractions

\frac{3}{3} - \frac{4 3}{3} : - 3

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{3 - 4 3}{3}

Add similar elements:

3 - 43 = - 33

= \frac{- 3 3}{3}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{3 3}{3}

Divide the numbers:

\frac{3}{3} = 1

= - 3

= 4 - 3

= 4 - 3

arctan (0.86)

- π^{2} cos (π (2))

- 2 (- 2 sec^{2} (0) + 3 sec^{4} (0))

2 sec (3 0^{\circ})

sin (\frac{60}{2})

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