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Poppii
@Poppii
August 2022
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помогите пожалуйста,очень срочно надо
[tex]3 cos^{2}x-4sinx*cosx-7 sin^{2} =0[/tex]
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hlopushinairina
3cos²x-4sinxcosx-7sin²x=0;⇒делим на cos²x;x≠π/2+kπ;
3-4tgx-7tg²x=0;⇒tgx=z;⇒
7z²+4z-3=0;⇒
z₁,₂=[-4⁺₋√(16+4·7·3)]/14=(-4⁺₋√100)/14=(-4⁺₋10)/14;
z₁=(-4+10)/14=6/14=3/7;⇒
tgx=3/7;
x=arctg3/7+kπ;k∈Z;
z₂=-14/14=-1;⇒
tgx=-1;
x=-π/4+2kπ;k∈Z;
x=3/4·π+2kπ;k∈Z
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Answers & Comments
3-4tgx-7tg²x=0;⇒tgx=z;⇒
7z²+4z-3=0;⇒
z₁,₂=[-4⁺₋√(16+4·7·3)]/14=(-4⁺₋√100)/14=(-4⁺₋10)/14;
z₁=(-4+10)/14=6/14=3/7;⇒
tgx=3/7;
x=arctg3/7+kπ;k∈Z;
z₂=-14/14=-1;⇒
tgx=-1;
x=-π/4+2kπ;k∈Z;
x=3/4·π+2kπ;k∈Z