Question

The value of $e^{\log_{10}{\tan 1}{^\circ} + \log_{10}{\tan 2}{^\circ} + \log_{10}{\tan 3}{^\circ} + ........... + \log_{10}{\tan 8}9{^\circ}}$ is

• A. 0
• B. e
• C. 1/e
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

We have $e^{\log_{10}\tan 1^{o} + \log_{10}\tan 2^{o} + \log_{10}\tan 3^{o} + .......... + \log_{10}\tan 89^{o}}$

$= e^{\log_{10}(\tan 1^{o}\tan 2^{o}\tan 3^{o}.....\tan 89^{o})} = e^{\log_{10}1} = e^{o} = 1$