The Value of logtan10+logtan20+??+logtan890 is -1 0 1/2 1 = log tan 1 0 + log ta

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Question
The Value of logtan10+logtan20+??+logtan890 is
Options
A. -1
B. 0
C. 1/2
D. 1

Correct Answer

0

Explanation

$= [\log \tan (1^{0}) + \log \tan (89^{0})] + [\log \tan (2^{0}) + \log \tan (88^{0})] + ? ? + [\log \tan (45^{0})]$

$= \log [\tan (1^{0}) � \tan (89^{0})] + \log [\tan (2^{0}) � \tan (88^{0})] + ? ? + \log (1)$

$[? \tan (90 - ?) = c o t ? a n d \tan (45^{0}) = 1]$

= log 1 + log 1 +.....+log 1

= 0.

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