AP EAMCET · Maths · Trigonometric Ratios & Identities
If \(\cos ^3 80^{\circ}+\cos ^3 40^{\circ}-\cos ^3 20^{\circ}=\mathrm{k}\), then \(\frac{4 \mathrm{k}}{3}=\)
- A \(\sin \left(\frac{4 \pi}{3}\right)\)
- B \(\cos \left(\frac{2 \pi}{3}\right)\)
- C \(\tan \left(\frac{\pi}{3}\right)\)
- D \(\sec \left(\frac{2 \pi}{3}\right)\)
Answer & Solution
Correct Answer
(B) \(\cos \left(\frac{2 \pi}{3}\right)\)
Step-by-step Solution
Detailed explanation
\(4k = 4(\cos^3 80^{\circ} + \cos^3 40^{\circ} - \cos^3 20^{\circ})\) \(4k = (\cos(3 \cdot 80^{\circ}) + 3\cos 80^{\circ}) + (\cos(3 \cdot 40^{\circ}) + 3\cos 40^{\circ}) - (\cos(3 \cdot 20^{\circ}) + 3\cos 20^{\circ})\)…
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