Question

Помогите, пожалуйста, решить tg170*tg160+1

Answer 1

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