What is the value of sec(pi/3)tan(pi/3) ?

The value of sec(pi/3)tan(pi/3) is 2sqrt(3)

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sec(pi/3)tan(pi/3)

sec (\frac{π}{3}) tan (\frac{π}{3})

23

Decimal Notation

3.46410 \dots

Solution steps

sec (\frac{π}{3}) tan (\frac{π}{3})

Use the following trivial identity:

sec (\frac{π}{3}) = 2

sec (\frac{π}{3})

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:

tan (\frac{π}{3}) = 3

tan (\frac{π}{3})

tan (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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 3

= 23

csc (arctan (- 2))

2 sin (\frac{4 π}{3})

csc (10 5^{\circ})

cos (2) (\frac{π}{2})

arcsin (- \frac{1}{4})

What is the value of sec(pi/3)tan(pi/3) ?
The value of sec(pi/3)tan(pi/3) is 2sqrt(3)