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