Question

sin^2 x+cos(60°+x)cos(60°-x)=1/4

Answer 1

cosa*cosb=1/2cos(a-b)+1/2cos(a+b)
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sin²x+cos(60+x)cos(60-x)=1/4
sin²x+1/2*cos2x+1/2cos120=1/4
sin²x+1/2*(1-2sin²x)+1/2*cos(180-60)=1/4
sin²x+1/2-sin²x+1/2*(-1/2)=1/4
1/2-1/4=1/4
1/4=1/4