Correct Answer - Option 2 : 1/8
Given:
cos 20° ⨯ cos 40° ⨯ cos 80°
Formula used:
cos (60 - x) cos x cos (60 + x) = (1/4) cos 3x
Calculations:
As we know, cos (60 - x) cos x cos (60 + x) = (1/4) cos 3x
Put x = 20°
cos (60 - 20) cos 20° cos (60 + 20) = (1/4) cos (3 × 20)
⇒ cos 40° ⨯ cos 20° ⨯ cos 80° = (1/4) × cos 60°
⇒ cos 20° ⨯ cos 40° ⨯ cos 80° = (1/4) × (1/2)
= 1/8
∴ The value of cos 20° ⨯ cos 40°⨯ cos 80° is 1/8.
