Multiple choice

$Find the value of ( \cot 25^{\circ} \cot 35^{\circ} \cot 45^{\circ} \cot 55^{\circ} \cot 65^{\circ} )$

  1. 1

  2. 0

  3. 3

  4. 4
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A Correct answer
Explanation

Use complementary angle identity: cot(θ) = tan(90°-θ). So cot 25° = tan 65°, cot 35° = tan 55°. The expression becomes tan 65° × tan 55° × cot 45° × cot 55° × cot 65°. Since cot 45° = 1 and tan θ × cot θ = 1, we get tan 65° × cot 65° × tan 55° × cot 55° × 1 = 1 × 1 × 1 = 1.

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