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slojno777
@slojno777
July 2022
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5cosx+2sinx=3
решите пожалуйста
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sedinalana
Verified answer
5cos²x/2-5sin²x/2+4sinx/2cosx/2-3sin²x/2-3cos²x/2=0/cos²x/2
8tg²x/2-4tgx/2-2=0
tgx/2=a
8a²-4a-2=0
D=16+64=80
a1=(4-4√5)/16=(1-√5)/4⇒tgx/2=(1-√5)/4⇒
x/2=arctg(1-√5)/4+πn⇒x=2arctg(1-√5)/4+2πn,n∈z
a2=(1+√5)/4⇒tgx/2=(1+√5)/4⇒x/2=arctg(1+√5)/4+πk⇒ x=2arctg(1+√5)/4+2πk,k∈z
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Answers & Comments
Verified answer
5cos²x/2-5sin²x/2+4sinx/2cosx/2-3sin²x/2-3cos²x/2=0/cos²x/28tg²x/2-4tgx/2-2=0
tgx/2=a
8a²-4a-2=0
D=16+64=80
a1=(4-4√5)/16=(1-√5)/4⇒tgx/2=(1-√5)/4⇒
x/2=arctg(1-√5)/4+πn⇒x=2arctg(1-√5)/4+2πn,n∈z
a2=(1+√5)/4⇒tgx/2=(1+√5)/4⇒x/2=arctg(1+√5)/4+πk⇒ x=2arctg(1+√5)/4+2πk,k∈z