The-value-of-e-log-10-tan-1-log-10-tan-2-log-10-tan-3-log-10-tan-89-is-

Question Number 101082 by 67549972 last updated on 30/Jun/20

The value of

e^{\log_{10} \tan 1 ° + \log_{10} \tan 2 ° + \log_{10} \tan 3 ° + \dots + \log_{10} \tan 89 °}

is

Commented by Dwaipayan Shikari last updated on 30/Jun/20

e^{{l o g}_{10} (t a n 1 ° t a n 2 ° t a n 3 ° \dots . . t a n 89 °)}

e^{{l o g}_{10} 1} = e^{0} = 1 {t a n 1 ° \dots t a n 89 ° = 1

Commented by smridha last updated on 01/Jul/20

e^{{l o g}_{10} [t a n 1^{°} . t a n 2^{°} . t a n 3^{°} \dots t a n 89^{°}]}

= e^{{l o g}_{10} [t a n 1^{°} . t a n 2^{°} . t a n 3 ° \dots c o t 3^{°} . c o t 2^{°} . c o t 1^{°}]}

= e^{{l o g}_{10} 1} = e^{0} = 1 .

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