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What will be the value of $cot 12 ° cot 38 ° cot 52 ° cot 60 ° cot 78 °$ ?

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12

23

13

32

answer is C.

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Detailed Solution

Given that

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

.
We use,

tan θ cot θ = 1 cot (90 ° − θ) = tan θ

Now,

= cot (90 − 78) ° cot (90 − 52) ° cot 52 ° cot 60 ° cot 78 °

= tan 78 ° tan 52 ° cot 52 ° cot 60 ° cot 78 °

= tan 78 ° cot 78 ° tan 52 ° cot 52 ° cot 60 °

= 1 × 1 × 13

= 13

Thus the value of

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

will be

13

.
Therefore the correct option is 3.

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