Option 1 : 6

**Given:**

(1 + tan23°)(1 + tan22°) + (1 + tan20°)(1 + tan25°) + (1 + tan29°)(1 + tan16°)

**Formula Used:**

If x + y = 45°

⇒ tan(x + y) = 1

⇒ (tanx + tany)/(1 – tanxtany) = 1

⇒ tanx + tany = 1 – tanxtany

⇒ tanx + tany + tanxtany = 1

⇒ 1 + tanx + tany + tanxtany = 1 + 1

⇒ (1 + tanx) + tany(1 + tanx) = 2

⇒ (1 + tanx)(1 + tany) = 2

**Calculation:**

(1 + tan23°)(1 + tan22°) + (1 + tan20°)(1 + tan25°) + (1 + tan29°)(1 + tan16°)

**Here, **

23° + 22° = 45°

⇒ (1 + tan23°)(1 + tan22°) = 2

20° + 25° = 45°

⇒ (1 + tan20°)(1 + tan25°) = 2

29° + 16° = 45°

⇒ (1 + tan29°)(1 + tan16°) = 2

Therefore, (1 + tan23°)(1 + tan22°) + (1 + tan20°)(1 + tan25°) + (1 + tan29°)(1 + tan16°)

⇒ 2 + 2 + 2

⇒ 6

**∴ The correct answer is 6**