23.9 a) (sin^2(x-pi/4)-1/2)(cos2x+1)=0;

Question

23.9 a) (sin^2(x-pi/4)-1/2)(cos2x+1)=0;

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Answer 1

(sin²(x-π/4)-1/2)(cos2x+1)=0
sin²(x-π/4)=1/2
(1-cos(2x-π/2))/2=1/2
1-cos(x-π/2)=1
cos(x-π/2)=0
sinx=0⇒x=πn
cos2x=-1
2x=π+2πn
x=π/2+πn