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

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(A) We are given the expression: $	an 1^{\circ} 	an 2^{\circ} 	an 3^{\circ} \cdots 	an 89^{\circ}$.Using the trigonometric identity $	an(90^{\cir

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$1$

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(A) We are given the expression: $	an 1^{\circ} 	an 2^{\circ} 	an 3^{\circ} \cdots 	an 89^{\circ}$.Using the trigonometric identity $	an(90^{\circ} - 	heta) = \cot 	heta$,we can rewrite the terms from $46^{\circ}$ to $89^{\circ}$ as:$	an 89^{\circ} = \cot 1^{\circ}$,$	an 88^{\circ} = \cot 2^{\circ}$,...,$	an 46^{\circ} = \cot 44^{\circ}$.Substituting these into the expression:$= (	an 1^{\circ} 	an 2^{\circ} \cdots 	an 44^{\circ}) \cdot 	an 45^{\circ} \cdot (	an 46^{\circ} \cdots 	an 88^{\circ} 	an 89^{\circ})$$= (	an 1^{\circ} 	an 2^{\circ} \cdots 	an 44^{\circ}) \cdot 1 \cdot (\cot 44^{\circ} \cdots \cot 2^{\circ} \cot 1^{\circ})$Since $	an 	heta \cdot \cot 	heta = 1$,the product of each pair $(	an 	heta \cdot \cot 	heta)$ is $1$.$= 1 \cdot 1 \cdot 1 \cdots 1 = 1$.

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

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