If , then is equal…

MATHEMATICS · Subjective · A Level · Mathematics · Trigonometry · Trigonometry

Problem

If 1sin⁡20∘+13cos⁡20∘=2kcos⁡40∘\frac{1}{\sin 20^\circ} + \frac{1}{\sqrt{3} \cos 20^\circ} = 2k \cos 40^\circ , then 18k4+162k2+36918k^4 + 162k^2 + 369 is equal to

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