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

The value of sec(30)+csc(60) is (4sqrt(3))/3

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sec(30)+csc(60)

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

\frac{4 3}{3}

Decimal Notation

2.30940 \dots

Solution steps

sec (3 0^{\circ}) + csc (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:

csc (6 0^{\circ}) = \frac{2 3}{3}

csc (6 0^{\circ})

csc (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} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 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} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

= \frac{2 3}{3}

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

Simplify

\frac{2 3}{3} + \frac{2 3}{3} : \frac{4 3}{3}

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

Apply rule

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

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

Add similar elements:

23 + 23 = 43

= \frac{4 3}{3}

= \frac{4 3}{3}

\frac{1}{sin ( \frac{1}{2} )}

cot (33.4 7^{\circ})

sin (- 59 0^{\circ})

\frac{51. 4 ^{2} sin ^{2} ( 2 3 ^{\circ} )}{2 ( 9.8 )}

\frac{π \cdot 98 \cdot 1169096}{60 \cdot 1000 \cdot cos ( 1 7 ^{\circ} )}

What is the value of sec(30)+csc(60) ?
The value of sec(30)+csc(60) is (4sqrt(3))/3