Question

$4sin^275* cos^275-( sin^275-cos^275)^2$

Answer 1

$4sin^2 75^o*cos^2 75^o=(2sin 75^o cos 75^o)^2=\(sin(2*75^o))^2=(sin 150^o)^2=0.5^2=0.25$

$(sin^2 75^o-cos^2 75^o)^2=(cos^2 75^o-sin^2 75^o)^2=\\(cos(2*75^o))^2=(cos 150^o)^2=(-frac{sqrt{3}}{2})^2=0.75$

$4sin^2 75^o*cos^2 75^o-(sin^2 75^o-cos^2 75^o)^2=0.25-0.75=-0.5$