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

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

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2sec(pi/4)+4cot(pi/3)

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

22 + \frac{4 3}{3}

Decimal Notation

5.13782 \dots

Solution steps

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

Use the following trivial identity:

sec (\frac{π}{4}) = 2

sec (\frac{π}{4})

sec (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} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} 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} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

= 2

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}

= 22 + 4 \cdot \frac{3}{3}

Simplify

22 + 4 \cdot \frac{3}{3} : 22 + \frac{4 3}{3}

22 + 4 \cdot \frac{3}{3}

Multiply

4 \cdot \frac{3}{3} : \frac{4 3}{3}

4 \cdot \frac{3}{3}

Multiply fractions:

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

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

= 22 + \frac{4 3}{3}

= 22 + \frac{4 3}{3}

arccsc (- 9)

300 sin (4 5^{\circ})

sin (4 \cdot \frac{π}{3})

cosh (i \frac{π}{4})

sin (2 0^{\circ}) \cdot 2

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