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sashenika
@sashenika
August 2022
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решите пожалуйста только 5 и 6
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hlopushinairina
5)4sin²2x+sin²4x=2 ⇒4sin²2x+4sin²2x·cos²2x=2 ⇒4sin²2x+4sin²2x(1-sin²2x)=2 ⇒
8sin²2x-4sin⁴2x-2=0 ⇒ sin²2x=z ⇒ 8z-4z²-2=0 ⇒2z²-4z+1=0
z₁,₂=(2⁺₋√4-4·2·1)/4 ⇒ D<0 ⇒корней нет
6)1-sin⁴x-5/3·cos⁴x=0 ⇒cos⁴x-5/3cos⁴x=0⇒ -2/3cos⁴x=0 ;⇒
cos⁴x=0 ;cosx=0 ⇒x=π/2+kπ,k∈Z
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Answers & Comments
8sin²2x-4sin⁴2x-2=0 ⇒ sin²2x=z ⇒ 8z-4z²-2=0 ⇒2z²-4z+1=0
z₁,₂=(2⁺₋√4-4·2·1)/4 ⇒ D<0 ⇒корней нет
6)1-sin⁴x-5/3·cos⁴x=0 ⇒cos⁴x-5/3cos⁴x=0⇒ -2/3cos⁴x=0 ;⇒
cos⁴x=0 ;cosx=0 ⇒x=π/2+kπ,k∈Z