What is the value of (8csc(30))/((2sec(60))) ?

The value of (8csc(30))/((2sec(60))) is 4

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(8csc(30))/((2sec(60)))

\frac{8 csc ( 3 0 ^{\circ} )}{( 2 sec ( 6 0 ^{\circ} ) )}

4

Solution steps

\frac{8 csc ( 3 0 ^{\circ} )}{( 2 sec ( 6 0 ^{\circ} ) )}

= \frac{8 csc ( 3 0 ^{\circ} )}{2 sec ( 6 0 ^{\circ} )}

Use the following trivial identity:

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

csc (3 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

= 2

Use the following trivial identity:

sec (6 0^{\circ}) = 2

sec (6 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}

= 2

= \frac{8 \cdot 2}{2 \cdot 2}

Simplify

= 4

\frac{π}{2} sin^{2} (\frac{1}{2})

sin (55. 9^{\circ})

\frac{530.37 ( 6.39 ) sin ( 51. 1 ^{\circ} )}{2 ( \frac{1}{60} )}

13 \cdot sin (3 0^{\circ})

- cos (\frac{π}{6} + \frac{π}{6})

What is the value of (8csc(30))/((2sec(60))) ?
The value of (8csc(30))/((2sec(60))) is 4