Find the value of, 8cos10°. cos20°. cos40° = ?

Answer: Option D

Let x = 8cos10°. cos20°. cos40°
Multiply on both side by sin10° and applying formula (2sinθ. cosθ = sin²θ)
⇒ x sin10° = 4 × 2sin10° cos10°. cos20°. cos40°
⇒ x sin10° = 2 × 2sin20°.cos20°. cos40°
⇒ x sin10° = 2 × sin40°. cos40°
⇒ x sin10° = sin80°
⇒ x sin10° = sin(90° - 10°)
⇒ x sin10° = cos10°
then, x = $$\frac{\cos {10}^{\circ }}{\sin {10}^{\circ }}$$
x = cot10°