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MashaBaggins
@MashaBaggins
August 2022
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Помогите решить уравнение, пожалуйста.
20.10 а
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sedinalana
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1+√3tgx≠0⇒√3tgx≠-1⇒tgx≠-1/√3⇒x≠-π/6+πn,n∈z
√3-tgx=1+√3tgx
√3tgx+tgx=√3-1
tgx(√3+1)=√3-1
tgx=(√3-1)/(√3+1)=(√3-1)²/(√3+1)(√3-1)=(3-2√3+1)/(3-1)=(4-2√3)/2=2-√3
x=arctg(2-√3)+πn,n∈z
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Answers & Comments
Verified answer
1+√3tgx≠0⇒√3tgx≠-1⇒tgx≠-1/√3⇒x≠-π/6+πn,n∈z√3-tgx=1+√3tgx
√3tgx+tgx=√3-1
tgx(√3+1)=√3-1
tgx=(√3-1)/(√3+1)=(√3-1)²/(√3+1)(√3-1)=(3-2√3+1)/(3-1)=(4-2√3)/2=2-√3
x=arctg(2-√3)+πn,n∈z