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

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(D) We know that $	an(90^\circ - 	heta) = \cot 	heta$. Given expression is $E = 	an 1^\circ 	an 2^\circ 	an 3^\circ \dots 	an 44^\circ 	an 45^

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$1$

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(D) We know that $	an(90^\circ - 	heta) = \cot 	heta$. Given expression is $E = 	an 1^\circ 	an 2^\circ 	an 3^\circ \dots 	an 44^\circ 	an 45^\circ 	an 46^\circ \dots 	an 88^\circ 	an 89^\circ$. We can pair the terms as: $(	an 1^\circ 	an 89^\circ) 	imes (	an 2^\circ 	an 88^\circ) 	imes \dots 	imes (	an 44^\circ 	an 46^\circ) 	imes 	an 45^\circ$. Since $	an 89^\circ = 	an(90^\circ - 1^\circ) = \cot 1^\circ$,we have $	an 1^\circ 	an 89^\circ = 	an 1^\circ \cot 1^\circ = 1$. Similarly,$	an k^\circ 	an(90^\circ - k^\circ) = 1$ for all $k$ from $1$ to $44$. Thus,$E = 1 	imes 1 	imes \dots 	imes 1 	imes 	an 45^\circ = 1 	imes 1 = 1$.

The value of $\tan 1^\circ \tan 2^\circ \tan 3^\circ \dots \tan 89^\circ$ is equal to

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