Question

evaluate cot12 cot38 cot52 cot60 cot78

Answer 1

This arrangement can be rearranged as :
(cot12*cot72)(cot38*cot52)cot 60
= {cot12*cot(90-12)}{cot38*cot(90-38) cot 60
= cot 12 * tan 12 * cot 38 * tan 38 *cot 60
= 1*1* cot 60
= cot 60 
= 1/2

Answer 2

Answer:

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

Step-by-step explanation:

cot 12° = cot (90-78) = tan 78°

cot 38° = cot (90-52) = tan 52°

cot 60° = $\frac{1 }{\sqrt{3} }$

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 × $\frac{1 }{\sqrt{3} }$

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