Question

Evaluate cot12°cot38°cot52°cot60°cot78°​

Answer 1

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$cot12° cot38° cot52° cot60° cot78°= \frac{1 }{\sqrt{3} }31$

Step-by-step explanation:

$cot 12° = cot (90-78) = tan 78°$

$cot 38° = cot (90-52) = tan 52°$

$60° = \frac{1 }{\sqrt{3} } 31$

Remember ⇒ cot∅ × tan∅ = 1

Applying all these theories in the question

cot 12° × cot 38° × cot 52° × cot 60° × cot 78°

Rearranging this equation,

( cot 78° × cot 12° ) × ( cot 52° × cot 38° ) × cot 60°

$= 1 × 1 × \frac{1 }{\sqrt{3} }31$

$= \frac{1 }{\sqrt{3} }31$