The value of

tan 5° tan 25° tan 45° tan 65° tan 85° is equal to:

Correct option is A

Given:

tan 5° tan 85° tan 25° tan 65° tan 45°

Concept Used:

tan (90° - θ) = cot θ

tan θ $$\times$$​cot θ = 1

tan 45° = 1

Solution:

Since,  tan 85° = cot (90° - 85°) = cot 5°

tan 65° = cot (90° - 65°) = cot 25°

Now,

= (tan 5° cot 5°) $$\times$$​ (tan 25° cot 25°)$$\times$$tan 45°

= 1$$\times$$ 1 $$\times$$ 1 = 1