What is the value of -2cos((2pi)/3)csc(((pi/3))/2) ?

The value of -2cos((2pi)/3)csc(((pi/3))/2) is 2

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-2cos((2pi)/3)csc(((pi/3))/2)

- 2 cos (\frac{2 π}{3}) csc (\frac{( \frac{π}{3} )}{2})

2

Solution steps

- 2 cos (\frac{2 π}{3}) csc (\frac{( \frac{π}{3} )}{2})

= - 2 cos (\frac{2 π}{3}) csc (\frac{\frac{π}{3}}{2})

Simplify:

\frac{\frac{π}{3}}{2} = \frac{π}{6}

= - 2 cos (\frac{2 π}{3}) csc (\frac{π}{6})

Use the following trivial identity:

cos (\frac{2 π}{3}) = - \frac{1}{2}

Use the following trivial identity:

csc (\frac{π}{6}) = 2

= - 2 (- \frac{1}{2}) \cdot 2

Simplify

- 2 (- \frac{1}{2}) \cdot 2 : 2

= 2

\frac{1}{2} (7) (10) (cos (\frac{π}{4})) (- \frac{π}{45})

3 \cdot cot (\frac{45}{2}) \cdot cot (\frac{75}{2}) \cdot cot (\frac{60}{2})

\frac{sin ( 30 0 ^{\circ} ) + cos ( 15 0 ^{\circ} )}{tan ( 12 0 ^{\circ} ) + cot ( 24 0 ^{\circ} )}

sin (\frac{π}{4}) cos (\frac{π}{3}) - cos (\frac{π}{4}) sin (\frac{π}{3})

4983 \cdot cos (4 0^{\circ})

What is the value of -2cos((2pi)/3)csc(((pi/3))/2) ?
The value of -2cos((2pi)/3)csc(((pi/3))/2) is 2