The value of tan 5^{circ} cdot tan 25^{circ} | vedclass

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(C) Given expression: $	an 5^{\circ} \cdot 	an 25^{\circ} \cdot 	an 45^{\circ} \cdot 	an 65^{\circ} \cdot 	an 85^{\circ}$We know that $	an 45^{\

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$1$

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(C) Given expression: $	an 5^{\circ} \cdot 	an 25^{\circ} \cdot 	an 45^{\circ} \cdot 	an 65^{\circ} \cdot 	an 85^{\circ}$We know that $	an 45^{\circ} = 1$ and $	an(90^{\circ} - 	heta) = \cot 	heta$.Substituting these values:$= 	an 5^{\circ} \cdot 	an 25^{\circ} \cdot 1 \cdot 	an(90^{\circ} - 25^{\circ}) \cdot 	an(90^{\circ} - 5^{\circ})$$= 	an 5^{\circ} \cdot 	an 25^{\circ} \cdot 1 \cdot \cot 25^{\circ} \cdot \cot 5^{\circ}$Since $	an 	heta \cdot \cot 	heta = 1$,we group the terms:$= (	an 5^{\circ} \cdot \cot 5^{\circ}) \cdot (	an 25^{\circ} \cdot \cot 25^{\circ}) \cdot 1$$= 1 \cdot 1 \cdot 1 = 1$

The value of $\tan 5^{\circ} \cdot \tan 25^{\circ} \cdot \tan 45^{\circ} \cdot \tan 65^{\circ} \cdot \tan 85^{\circ}$ is $\ldots \ldots \ldots \ldots .$.

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