The value of {e^{{{log }_{10}}tan 1^circ + {{ | vedclass

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(D) Let $S = 	an 1^\circ \cdot 	an 2^\circ \cdot 	an 3^\circ \cdot \dots \cdot 	an 89^\circ$. Using the property $	an 	heta \cdot 	an(90^\circ

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$1$

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(D) Let $S = 	an 1^\circ \cdot 	an 2^\circ \cdot 	an 3^\circ \cdot \dots \cdot 	an 89^\circ$. Using the property $	an 	heta \cdot 	an(90^\circ - 	heta) = 1$,we can pair the terms: $(	an 1^\circ \cdot 	an 89^\circ) \cdot (	an 2^\circ \cdot 	an 88^\circ) \cdot \dots \cdot (	an 44^\circ \cdot 	an 46^\circ) \cdot 	an 45^\circ$. Each pair equals $1$,and $	an 45^\circ = 1$. Thus,$S = 1$. The expression is $e^{\log_{10}(S)} = e^{\log_{10}(1)} = e^0 = 1$.

The value of ${e^{{{\log }_{10}}\tan 1^\circ + {{\log }_{10}}\tan 2^\circ + {{\log }_{10}}\tan 3^\circ + ........... + {{\log }_{10}}\tan 89^\circ }}$ is

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