What is the value of sec((2pi)/3)-tan(pi/6) ?

The value of sec((2pi)/3)-tan(pi/6) is -2-(sqrt(3))/3

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sec((2pi)/3)-tan(pi/6)

sec (\frac{2 π}{3}) - tan (\frac{π}{6})

- 2 - \frac{3}{3}

Decimal Notation

- 2.57735 \dots

Solution steps

sec (\frac{2 π}{3}) - tan (\frac{π}{6})

Use the following trivial identity:

sec (\frac{2 π}{3}) = - 2

sec (\frac{2 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}{6}) = \frac{3}{3}

tan (\frac{π}{6})

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}

= \frac{3}{3}

= - 2 - \frac{3}{3}

3 \cdot cos (\frac{π}{2})

1 + cos (\frac{π}{6})

1 - sin^{2} (6 0^{\circ})

4 + 3 cos (- \frac{π}{6})

cos (2 π^{50}) \cdot \frac{100}{π}

What is the value of sec((2pi)/3)-tan(pi/6) ?
The value of sec((2pi)/3)-tan(pi/6) is -2-(sqrt(3))/3