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Question

Find the value of the expression
cot 12× cot 38× cot 52× cot 60× cot 78.

A
23
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B
12
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C
13
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D
1
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Solution

The correct option is C 13
Given: cot 12× cot 38× cot 52× cot 60× cot 78

On rearranging the given equation we get,
=(cot 12×cot 78)×(cot 38×cot 52)×cot 60

={cot 12×cot(9012)}{cot 38×cot(9038)}×cot 60

We know that, cot (90θ)=tan θ.
Hence, cot (9012)=tan 12,
cot (9038)=tan 38 and cot 60=13
On substituting these values we get,

=(cot 12×tan 12)×(cot 38×tan 38)×13

=1×1×13=13.....[cot θ×tan θ=1] .
The value of the expression
cot 12× cot 38× cot 52× cot 60× cot 78=13.

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