1+tg^2*a=1/cos^2*a 1+ctg^*2=1/sin^2*a докажите - вопрос №881536212121212 от shootdm100 13.02.2021 13:46

Question

Математика: 1+tg^2*a=1/cos^2*a 1+ctg^*2=1/sin^2*a докажите !

shootdm100 · Answer

А) 1+tg²@=1/cos²@
1 + sin²@/cos²@ = 1/cos²@
1 + (1-cos²@)/cos²@) = 1/cos²@
(cos²@ + 1 - cos²@)/cos²@ = 1/cos²@
1/cos²@ = 1/cos²@, ч.т.д.
б) 1+ctg²@=1/sin²@
1 + cos²@/sin²@ = 1/sin²@
1 + (1-sin²@)/sin²@) = 1/sin²@
(sin²@ + 1 - sin²@)/sin²@ = 1/sin²@
1/sin²@ = 1/sin²@, ч.т.д.