помогите, пожалуйста, решить tg170*tg160+1. Created by elvirasalavatova. matematika-ru

помогите, пожалуйста, решить tg170*tg160+1...

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помогите, пожалуйста, решить
tg170*tg160+1

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ruslank1460

tg170°*tg160°+1 = tg(180° - 10°)tg(180° - 20°) +1 = tg 10° tg20° +1 = tg 10° $\frac{2tg10^{0}}{1-tg^210^{0}} +1 = \frac{2tg^210^{0}+1-tg^210^{0}}{1-tg^210^{0}} = \frac{tg^210^{0}+1}{1-tg^210^{0}} = \frac{1}{cos20^{0}}$

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