15*(1/20*21+1/21*22+1/22*23+1/23*24+1/24*25+1/25*26+1/26*27+1/27*28+1/28*29+1/29*30) - id1340047620220501 от tanyaanya200615 01.05.2022 09:03

Question

Математика: 15*(1/20*21+1/21*22+1/22*23+1/23*24+1/24*25+1/25*26+1/26*27+1/27*28+1/28*29+1/29*30)​

tanyaanya200615 · Accepted Answer

6sinxcosx=5cos2x
6sinxcosx=5*(cos^2x - sin^2x)
6sinxcosx=5cos^2x - 5sin^2x
5sin^2x + 6cosxsinx - 5cos^2x = 0 /:cos^2x ≠ 0
однородное уравнение второй степени
5tg^2x + 6tgx - 5 = 0
Пусть tgx = t, причём t ∈ (- беск; + беск )
Тогда решим кв. уравнение:
5t^2 + 6t - 5 = 0
D = 36 + 4*5*5 = 36 + 100 = 136
√D = √136 = 2√34
t1 = ( - 6 + 2√34)/ 10 = ( - 3 + √34)/ 5
t2 = ( - 6 - 2√34)/ 10 = ( - 3 - √34)/ 5

tgx = ( - 3 + √34)/ 5
x = arctg ( - 3 + √34)/ 5 + pik, k ∈Z

tgx = ( - 3 - √34)/ 5
x = arctg ( - 3 - √34)/ 5 + pik, k ∈Z

15(1/2021+1/2122+1/2223+1/2324+1/2425+1/2526+1/2627+1/2728+1/2829+1/29*30)

MOGZ ответил

15*(1/20*21+1/21*22+1/22*23+1/23*24+1/24*25+1/25*26+1/26*27+1/27*28+1/28*29+1/29*30)​

MOGZ ответил

15(1/2021+1/2122+1/2223+1/2324+1/2425+1/2526+1/2627+1/2728+1/2829+1/29*30)