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sashaying
@sashaying
August 2022
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алгебра 10 класс
cos^8x+sin^3x=1
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Answers & Comments
RuLensk14
Cos^8x+sin^3x=sin^2x+cos^2x
cos^8x-cos^2x=sin^2x-sin^3x
cos^2x(cos^6x-1)=sin^2x(1-sinx)
(1-sinx)(1+sinx)(cos^6x-1)-sin^2x(1-sinx)=0
(1-sinx)((1-sinx)(cos^6x-1)-sin^2x)=0
1-sinx=0 => sinx=1
(1-sinx)(cos^6x-1)-sin^2x=0
-sin^6x(1-sinx)-sin^2x=0
-sin^2x(sin^4x+sin^5x+1)=0
-sin^2x=0
sin^4x+sin^5x+1=0
sin^4x(1+sin^x)+1=0
1 votes
Thanks 1
sashaying
В итоге 2 ответа должно получится , но тут я не особо поняла ( вижу только 1)
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Answers & Comments
cos^8x-cos^2x=sin^2x-sin^3x
cos^2x(cos^6x-1)=sin^2x(1-sinx)
(1-sinx)(1+sinx)(cos^6x-1)-sin^2x(1-sinx)=0
(1-sinx)((1-sinx)(cos^6x-1)-sin^2x)=0
1-sinx=0 => sinx=1
(1-sinx)(cos^6x-1)-sin^2x=0
-sin^6x(1-sinx)-sin^2x=0
-sin^2x(sin^4x+sin^5x+1)=0
-sin^2x=0
sin^4x+sin^5x+1=0
sin^4x(1+sin^x)+1=0