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

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

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$1$

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(C) We are given the expression: $	an 1^{\circ} 	an 2^{\circ} 	an 3^{\circ} \ldots 	an 89^{\circ}$.Using the identity $	an(90^{\circ} - 	heta) = \cot 	heta$,we can rewrite the terms:$	an 89^{\circ} = 	an(90^{\circ} - 1^{\circ}) = \cot 1^{\circ} = \frac{1}{	an 1^{\circ}}$.$	an 88^{\circ} = 	an(90^{\circ} - 2^{\circ}) = \cot 2^{\circ} = \frac{1}{	an 2^{\circ}}$.This pattern continues up to $	an 46^{\circ} = \cot 44^{\circ} = \frac{1}{	an 44^{\circ}}$.The middle term is $	an 45^{\circ} = 1$.Substituting these into the product:$(	an 1^{\circ} \cdot \cot 1^{\circ}) \cdot (	an 2^{\circ} \cdot \cot 2^{\circ}) \cdots (	an 44^{\circ} \cdot \cot 44^{\circ}) \cdot 	an 45^{\circ}$.Since $	an 	heta \cdot \cot 	heta = 1$,the product becomes $1 \cdot 1 \cdots 1 \cdot 1 = 1$.

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

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