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alihanbijiev
@alihanbijiev
July 2022
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Решите уравнение 10-11 класс номер 13 в пользу
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tseluykoln
13. 1+1/3 ^(ctgx)=4*3^(2*(cosxcosπ/4+sinx*sinπ/4)/√2sinx)
1+1/3^(ctgx)=4*3^((cosx+sinx)/sinx)
1+1/3^(ctgx)=4*3*3ctgx
3^ctgx=t, t>0
1+1/t=12t
12t²-t-1=0, t₁=-1/4 не удовлетворяет t₂=1/3
3^ctgx=1/3
ctgx=-1, x=3π/4+πn
б) -π/4;3π/4
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Answers & Comments
1+1/3^(ctgx)=4*3^((cosx+sinx)/sinx)
1+1/3^(ctgx)=4*3*3ctgx
3^ctgx=t, t>0
1+1/t=12t
12t²-t-1=0, t₁=-1/4 не удовлетворяет t₂=1/3
3^ctgx=1/3
ctgx=-1, x=3π/4+πn
б) -π/4;3π/4