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

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(D) Let the given expression be $X = e^{\log_{10} 	an 1^\circ + \log_{10} 	an 2^\circ + \dots + \log_{10} 	an 89^\circ}$.Using the property $\log a

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$1$

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(D) Let the given expression be $X = e^{\log_{10} 	an 1^\circ + \log_{10} 	an 2^\circ + \dots + \log_{10} 	an 89^\circ}$.Using the property $\log a + \log b = \log(ab)$,we get:$X = e^{\log_{10}(	an 1^\circ \cdot 	an 2^\circ \cdot 	an 3^\circ \cdot \dots \cdot 	an 89^\circ)}$.We know that $	an(90^\circ - 	heta) = \cot 	heta$,so $	an 89^\circ = \cot 1^\circ$,$	an 88^\circ = \cot 2^\circ$,and so on.The product $P = 	an 1^\circ \cdot 	an 2^\circ \cdot \dots \cdot 	an 44^\circ \cdot 	an 45^\circ \cdot 	an 46^\circ \cdot \dots \cdot 	an 89^\circ$.$P = (	an 1^\circ \cdot \cot 1^\circ) \cdot (	an 2^\circ \cdot \cot 2^\circ) \cdot \dots \cdot (	an 44^\circ \cdot \cot 44^\circ) \cdot 	an 45^\circ$.Since $	an 	heta \cdot \cot 	heta = 1$ and $	an 45^\circ = 1$,we have $P = 1 \cdot 1 \cdot \dots \cdot 1 = 1$.Thus,$X = e^{\log_{10}(1)} = e^0 = 1$.

The value of ${e^{\log_{10} \tan 1^\circ + \log_{10} \tan 2^\circ + \log_{10} \tan 3^\circ + \dots + \log_{10} \tan 89^\circ}}$ is

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