If-log-tan-1-log-tan-2-log-tan-3-log-tan-89-p-then-p-2-3-

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

I f \log \tan 1 ° + \log \tan 2 ° + \log \tan 3 ° + \dots + \log \tan 89 ° = p

t h e n p^{2} + 3 =

Answered by bobhans last updated on 25/Sep/20

\Rightarrow \log (\tan 1 ° \times \tan 2 ° \times \tan 3 ° \times \dots \times \tan 89 °) = p

c o n s i d e r \tan 89 ° \times \tan 1 ° = 1

\tan 88 ° \times \tan 2 ° = 1, s o o n . w e g e t

\log (1 \times 1 \times 1 \times 1 \times \dots \times 1) = p

\Rightarrow p = 0 t h e n p^{2} + 3 = 3

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