Question

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

Answer 1

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Answer 2

$\cot 12 \tan 38 \tan 52 \tan 60 \cot 78=\sqrt{3}$

Step-by-step explanation:

We have,

$\cot 12 \tan 38 \tan 52 \tan 60 \cot 78$

To find, $\cot 12 \tan 38 \tan 52 \tan 60 \cot 78=?$

=$\cot 12\times \tan 38\times \tan (90-38)\times \tan 60\times \cot (90-12)$

$=\cot 12\times \tan 38\times \cot 38\times \tan 60\times \tan 12$

$=(\tan 12\times \cot 12)\times (\tan 38\times \cot 38)\times \tan 60$

$=(1)\times (1)\times \tan 60$

[ ∵ $\tan A\times \cot A=1$]

$=\sqrt{3}$ [∵$\tan 60=\sqrt{3}$]

Hence, $\cot 12 \tan 38 \tan 52 \tan 60 \cot 78=\sqrt{3}$.