Question

Упрастите выражение: $frac{cos4alpha }{cos2alpha -sin2alpha}$

Answer 1

cos4α/(cos2α-sin2α)=cos4α*(cos2α+sin2α)/((cos2α-sin2α)(cos2α+sin2α)=

=cos4α*(sin2α+cos2α)/(cos²2α-sin²2α)=cos4α*(sin2α+cos2α)/cos4α=

=sin2α+cos2α.