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Question Number 115341 by bemath last updated on 25/Sep/20

$$If\log \tan 1°+\log \tan 2°+\log \tan 3°+...+\log \tan 89°=p$$$$then{p}^2+3=$$

Answered by bobhans last updated on 25/Sep/20

$$\Rightarrow \log (\tan 1°\times \tan 2°\times \tan 3°\times ...\times \tan 89°)=p$$$$consider\tan 89°\times \tan 1°=1$$$$\tan 88°\times \tan 2°=1,soon.weget$$$$\log (1\times 1\times 1\times 1\times ...\times 1)=p$$$$\Rightarrow p=0then{p}^2+3=3$$

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