tan-1-tan-5-tan-9-tan-173-tan-177-

Question Number 147651 by iloveisrael last updated on 22/Jul/21

\tan 1 ° + \tan 5 ° + \tan 9 ° + \dots + \tan 173 ° + \tan 177 ° = ?

Commented by mr W last updated on 22/Jul/21

= 45

Commented by iloveisrael last updated on 23/Jul/21

is the formula

\tan α + \tan (60 ° - α) + \tan (60 ° + α) = 3 \tan (3 α)

correct ?

Answered by mathmax by abdo last updated on 22/Jul/21

S = \tan (\frac{π}{180}) + \tan (\frac{5 π}{180}) + \tan (\frac{9 π}{180}) + \dots . + \tan (\frac{169 π}{180}) + \tan (\frac{173 π}{180}) + \tan (\frac{177 π}{180})

S = \tan (\frac{π}{180}) + \tan (\frac{5 π}{180}) + \tan (\frac{9 π}{180}) + \dots + \tan (π - \frac{9 π}{180}) + \tan (π - \frac{5 π}{180})

+ \tan (π - \frac{π}{190}) = 0