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yoorion
@yoorion
July 2022
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Tg^2x+3ctg^2x=4 на (120град; 180град) ПОМОГИТЕ, ПОЖАЛУЙСТА
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LyubaAlexandorovna
Tq^2(x)+3*ctq^2(x)=4 [2*П/3; П]
ctqx=1/tqx
tq^2(x)+3/tq^2(x)=4
ОДЗ х не равен П/2+П*n, nЄZ
Пусть tqx^2(x)=t t+3/t=4 t^2-4*t+3=0 t1,2=(4±√(4^2-4*3))/2=(4±2)/2
t=(4-2)/2=1 tq^2(x)=1 tq(x)=±1
x=П/4+П*n, nЄZ
x=3*П/4+П*k, kЄZ
t2=(4+2)/2=3 tq^2(x)=3 tqx=±√3
x=П/3+П*n, nЄZ
x=2*П/3+П*k, kЄZ
(2*П/3;П) х=3*П/4
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yoorion
Спасибо большое
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Answers & Comments
ctqx=1/tqx
tq^2(x)+3/tq^2(x)=4
ОДЗ х не равен П/2+П*n, nЄZ
Пусть tqx^2(x)=t t+3/t=4 t^2-4*t+3=0 t1,2=(4±√(4^2-4*3))/2=(4±2)/2
t=(4-2)/2=1 tq^2(x)=1 tq(x)=±1
x=П/4+П*n, nЄZ
x=3*П/4+П*k, kЄZ
t2=(4+2)/2=3 tq^2(x)=3 tqx=±√3
x=П/3+П*n, nЄZ
x=2*П/3+П*k, kЄZ
(2*П/3;П) х=3*П/4