log _{10} tan 40^{circ} cdot log _{10} tan 41 | vedclass

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Question

(B) The given expression is a product of logarithmic terms: $\log _{10} 	an 40^{\circ} \cdot \log _{10} 	an 41^{\circ} \cdots \log _{10} 	an 50^{\c

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(B) The given expression is a product of logarithmic terms: $\log _{10} 	an 40^{\circ} \cdot \log _{10} 	an 41^{\circ} \cdots \log _{10} 	an 50^{\circ}$.In this sequence,the term $\log _{10} 	an 45^{\circ}$ is included.We know that $	an 45^{\circ} = 1$.Therefore,$\log _{10} 	an 45^{\circ} = \log _{10} 1 = 0$.Since one of the factors in the product is $0$,the entire product becomes $0$.

$\log _{10} \tan 40^{\circ} \cdot \log _{10} \tan 41^{\circ} \cdots \log _{10} \tan 50^{\circ} = ?$

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