What is the value of sec(pi/6)+tan(pi/6) ?

The value of sec(pi/6)+tan(pi/6) is square root of 3

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sec(pi/6)+tan(pi/6)

sec (\frac{π}{6}) + tan (\frac{π}{6})

3

Decimal Notation

1.73205 \dots

Solution steps

sec (\frac{π}{6}) + tan (\frac{π}{6})

Use the following trivial identity:

sec (\frac{π}{6}) = \frac{2 3}{3}

sec (\frac{π}{6})

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}

= \frac{2 3}{3}

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}

= \frac{2 3}{3} + \frac{3}{3}

Simplify

\frac{2 3}{3} + \frac{3}{3} : 3

\frac{2 3}{3} + \frac{3}{3}

Apply rule

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

= \frac{2 3 + 3}{3}

Add similar elements:

23 + 3 = 33

= \frac{3 3}{3}

Divide the numbers:

\frac{3}{3} = 1

= 3

= 3

sin (6 0^{\circ}) + cos (4 5^{\circ})

sin (arctan (\frac{12}{5}) + arccos (\frac{12}{13}))

arcsin (0.4848)

- \frac{3}{8} cos (2) - \frac{3}{4} sin^{2} (1) + sin^{4} (1) + \frac{3}{8}

20 \cdot sin (3 5^{\circ})

What is the value of sec(pi/6)+tan(pi/6) ?
The value of sec(pi/6)+tan(pi/6) is square root of 3