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

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(B) The given expression is $E = 	an 1^{\circ} 	an 2^{\circ} \ldots 	an 44^{\circ} 	an 45^{\circ} 	an 46^{\circ} \ldots 	an 88^{\circ} 	an 89^{

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$1$

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(B) The given expression is $E = 	an 1^{\circ} 	an 2^{\circ} \ldots 	an 44^{\circ} 	an 45^{\circ} 	an 46^{\circ} \ldots 	an 88^{\circ} 	an 89^{\circ}$.We know that $	an(90^{\circ} - 	heta) = \cot 	heta$.Therefore,$	an 89^{\circ} = 	an(90^{\circ} - 1^{\circ}) = \cot 1^{\circ}$,$	an 88^{\circ} = \cot 2^{\circ}$,and so on.Substituting these values,we get $E = (	an 1^{\circ} \cot 1^{\circ}) (	an 2^{\circ} \cot 2^{\circ}) \ldots (	an 44^{\circ} \cot 44^{\circ}) 	an 45^{\circ}$.Since $	an 	heta \cdot \cot 	heta = 1$ and $	an 45^{\circ} = 1$,the expression becomes $1 \cdot 1 \cdot \ldots \cdot 1 = 1$.

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

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