The value of tan 1^{circ} tan 2^{circ} tan 3^ | vedclass

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(B) We are given the expression: $	an 1^{\circ} 	an 2^{\circ} 	an 3^{\circ} \ldots 	an 89^{\circ}$.Using the property $	an(90^{\circ} - 	heta) =

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$1$

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(B) We are given the expression: $	an 1^{\circ} 	an 2^{\circ} 	an 3^{\circ} \ldots 	an 89^{\circ}$.Using the property $	an(90^{\circ} - 	heta) = \cot 	heta$,we can rewrite the terms from $46^{\circ}$ to $89^{\circ}$ as:$	an 89^{\circ} = 	an(90^{\circ} - 1^{\circ}) = \cot 1^{\circ}$$	an 88^{\circ} = 	an(90^{\circ} - 2^{\circ}) = \cot 2^{\circ}$$\dots$$	an 46^{\circ} = 	an(90^{\circ} - 44^{\circ}) = \cot 44^{\circ}$.Substituting these into the expression:$= (	an 1^{\circ} \cot 1^{\circ}) 	imes (	an 2^{\circ} \cot 2^{\circ}) 	imes \dots 	imes (	an 44^{\circ} \cot 44^{\circ}) 	imes 	an 45^{\circ}$.Since $	an 	heta \cot 	heta = 1$ and $	an 45^{\circ} = 1$,the expression becomes:$= 1 	imes 1 	imes \dots 	imes 1 	imes 1 = 1$.

The value of $\tan 1^{\circ} \tan 2^{\circ} \tan 3^{\circ} \ldots \tan 89^{\circ}$ is

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