If $4k = an^2 60° - 2\csc^2 30° - 2 an^2 30°$, then find the value of $k$.

Question

If $4k = 	an^2 60° - 2\csc^2 30° - 2	an^2 30°$, then find the value of $k$.

Accepted Answer

Step 1: $4k = (\sqrt{3})^2 - 2(2)^2 - 2\left(\frac{1}{\sqrt{3}}\right)^2 = 3 - 8 - \frac{2}{3} = -\frac{17}{3}$
Step 2: $k = -\frac{17}{12}$

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