What is the value of (sin(30)*cos(60)*csc(45))/(tan(30)*sec(60)*cot(45)) ?

The value of (sin(30)*cos(60)*csc(45))/(tan(30)*sec(60)*cot(45)) is (sqrt(6))/8

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(sin(30)cos(60)csc(45))/(tan(30)sec(60)cot(45))

\frac{sin ( 3 0 ^{\circ} ) \cdot cos ( 6 0 ^{\circ} ) \cdot csc ( 4 5 ^{\circ} )}{tan ( 3 0 ^{\circ} ) \cdot sec ( 6 0 ^{\circ} ) \cdot cot ( 4 5 ^{\circ} )}

\frac{6}{8}

Solution steps

\frac{sin ( 3 0 ^{\circ} ) cos ( 6 0 ^{\circ} ) csc ( 4 5 ^{\circ} )}{tan ( 3 0 ^{\circ} ) sec ( 6 0 ^{\circ} ) cot ( 4 5 ^{\circ} )}

Use the following trivial identity:

sin (3 0^{\circ}) = \frac{1}{2}

Use the following trivial identity:

cos (6 0^{\circ}) = \frac{1}{2}

Use the following trivial identity:

csc (4 5^{\circ}) = 2

Use the following trivial identity:

tan (3 0^{\circ}) = \frac{3}{3}

Use the following trivial identity:

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

Use the following trivial identity:

cot (4 5^{\circ}) = 1

= \frac{\frac{1}{2} \cdot \frac{1}{2} 2}{\frac{3}{3} \cdot 2 \cdot 1}

Simplify

\frac{\frac{1}{2} \cdot \frac{1}{2} 2}{\frac{3}{3} \cdot 2 \cdot 1} : \frac{6}{8}

= \frac{6}{8}

tan^{2} (4 5^{\circ} - \frac{34}{2})

arctan (\frac{15}{7})

cos (arcsin (- \frac{8}{17}))

arctan (\frac{- 5}{- 6})

sin (23.5 8^{\circ})

What is the value of (sin(30)*cos(60)*csc(45))/(tan(30)*sec(60)*cot(45)) ?
The value of (sin(30)*cos(60)*csc(45))/(tan(30)*sec(60)*cot(45)) is (sqrt(6))/8