Question

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Answer 1

2Sin^2 x +(2 - √2)cosx + √2 - 2 = 0
2(1-сos^2 x) +(2 - √2)cosx + √2 - 2 = 0
2-2cos^2 x +(2 - √2)cosx + √2 - 2 = 0
-2cos^2 x +(2 - √2)cosx + √2 = 0
D=(2 - √2)^2-4*(-2)* √2=4-4 √2+2+8 √2=4+4 √2+2=(2+ √2)^2
 
cos x1=(-2+ √2+2+ √2)/(-4)=- √2/2
x1=(+/-)3pi/4+2*pi*k, k є Z
 
сos x2=(-2+ √2-2- √2)/(-4)=1
x2=2*pi*n, n є Z