Question

Преобразуйте выражение
$cos^{2} x-sin( frac{ pi }{6} -x)*sin (frac{ pi }{6} +x)$

Answer 1

$cos^{2} x-sin( frac{ pi }{6} -x)sin (frac{ pi }{6} +x)= \ =cos^{2} x-0,5(cos(frac{ pi }{6} -x-frac{ pi }{6} -x)-cos(frac{ pi }{6} -x+frac{ pi }{6} +x))= \ =cos^{2} x-0,5(cos2x-cosfrac{ pi }{3})=cos^{2} x-0,5(cos2x-0.5)= \ =cos^{2} x-0,5cos2x+0.25=cos^{2} x-0,5cos^2x+0.5sin^2x+0.25= \ =0,5cos^2x+0.5sin^2x+0.25=0.5+0.25=0.75$