Question

What is the value of cot 35° cot 40° cot 45° cot 50° cot 55°?

• A. 1
• B. 0
• C. 2
• D. -1

Answer 1

Answer:

A. 1

Solution:

Given:

cot 35° cot 40° cot 45° cot 50° cot 55°

Concept used:

cot 45^° = 1

tan θ × cot θ = 1

tan A = cot B, if A + B = 90^° 

Calculation:

cot 35° cot 40° cot 45° cot 50° cot 55°

⇒ cot 35^° cot 40^° cot 45^° tan 40^° tan 35^° 

⇒ cot 35^° tan 35^° cot 40^° tan 40^° cot 45^° 

⇒ cot 45^° = 1

∴ The correct answer is 1.