Practicing Success
Solve \(\frac{32cos^610° - 48cos^410° + 18cos^210° - 1}{4sin10° cos10° sin50° cos50° sin70° cos70°}\) |
\(\frac{8}{\sqrt {3}}\) 8\(\sqrt {3}\) \(\frac{4}{\sqrt {3}}\) 4\(\sqrt {3}\) |
\(\frac{8}{\sqrt {3}}\) |
\(\frac{2(cos^610° - 24cos^410° + 9cos10° ) - 1}{4 × \frac{1}{4}sin 3 × 10° × \frac{1}{4} × cos3 × 10° }\) ⇒ \(\frac{2 (4cos^310° - 3cos10° )^2 - 1}{4 × \frac{1}{4} × \frac{1}{2} × \frac{1}{4} × \frac{\sqrt {3}}{2} }\) (cos3θ = 4cos3 θ - 3cosθ) ⇒ \(\frac{2 × (cos3 θ)^2 - 1}{\frac{\sqrt {3}}{16}}\) ⇒ \(\frac{2 × cos^230 - 1}{\frac{\sqrt {3}}{16}}\) ⇒ \(\frac{2 × \frac{3}{4}- 1}{\frac{\sqrt {3}}{16}}\) = \(\frac{8}{\sqrt {3}}\) |