Question

Find the value of (cos18° cos42° cos78°) × (sin12° sin48° sin72°)^-1

1. -1
2. 1
3. 3
4. -3

Answer 1

Correct Answer - Option 2 : 1

Concept used:

cosθ × cos(60° – θ) × cos(60° + θ) = (1/4) × cos3θ

sinθ × sin(60° – θ) × sin(60° + θ) = (1/4) × sin3θ

sinθ = cos(90° - θ)

Calculations:

(cos18° cos42° cos60° cos78°) × (sin12° sin48° sin72°)^-1

⇒ (cos18° cos42° cos78°) × [(sin12° sin48° sin72°)]^-1

⇒ (cos18° cos(60° – 18°) cos(60° + 18°) × [(sin12° sin(60° – 12°) sin(60° + 12°)]^-1

⇒ (1/4) × (cos54°) × [(1/4) × sin36°]^-1

⇒ (1/4) cos54° × [(1/4) × cos54°]^-1 

⇒ [(1/4) cos54°]/[(1/4) cos54°]

⇒ 1

∴ The correct answer will be option 2.