Cos(4x)-sin^2(x)=1 !!!!!!!!!!!

Question

Cos(4x)-sin^2(x)=1
!!!!!!!!!!!

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Answer 1

2cos^2(2x)-1-sin^2(x)-1=0
2(2cos^2(x)-1)^2-(1-cos^2(x))-2=0
8cos^4(x)-8cos^2(x)+2-1+cos^2(x)-2=0
8cos^4(x)-7cos^2(x)-1=0
Cos^2(x)=t
8 t^2-7t-1=0
t=1. t=-1/8
Cos^2(x)=1
Cos x=1. Cos x =-1
X=2пk. X=П+2пk. Ответ: X=Пk