What is the value of sec(30)+cot(60) ?

The value of sec(30)+cot(60) is square root of 3

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sec(30)+cot(60)

sec (3 0^{\circ}) + cot (6 0^{\circ})

3

Decimal Notation

1.73205 \dots

Solution steps

sec (3 0^{\circ}) + cot (6 0^{\circ})

Use the following trivial identity:

sec (3 0^{\circ}) = \frac{2 3}{3}

sec (3 0^{\circ})

sec (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

= \frac{2 3}{3}

Use the following trivial identity:

cot (6 0^{\circ}) = \frac{3}{3}

cot (6 0^{\circ})

cot (x)

periodicity table with

18 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 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

csc (\frac{21 π}{10})

arctan (- \frac{23}{2})

sin (\frac{1}{\frac{2}{3 π}})

sin (1 5^{\circ}) cos (7 5^{\circ})

arctan (1.67)

What is the value of sec(30)+cot(60) ?
The value of sec(30)+cot(60) is square root of 3