1)(cos4a+cos2a)/(sin4a-sin2a)=2cos3acosa/2sinacos3a=cosa/sina=ctga
2)sin25sin5-0,5cos20=0,5cos20-0,5cos30-0,5cos20=-√3/4
3)(cosa+2cos2a+cos3a)/(sina+2sin2a+sin3a)=
=(2cos2acosa+2cos2a)/(2sin2acosa+2sin2a)=2cos2a(cosa+1)/2sin2a(cosa+1)=
=cos2a/sin2a=ctg2a
4)sin(π/4+a)*sin(3π/4+a)=1/2*cos(-π/2)-1/2cos(π+2a)=1/2*0-1/2*(-cos2a)=
=1/2cos2a
или
sin(π/4+a)-sin(3π/4+a)=2sin(-π/4)cos(π/2+a)=-2*√2/2*(-sina)=√2sina
5)2sin(a+b)*sin(a-b)+2cos²b-1=2*1/2(cos2b-cos2a)+cos2b=cos2b-cos2a+cos2b=
=2cos2b-cos2a
6)(2cos3a*cosa-cos2a)/(sin6a-sin2a)=[2*1/2(cos2a-cos4a)-cos2a]/2sin2acos4a=
=(cos2a-cos4a-cos2a)/2sin2acos4a=-cos4a/2sin2acos4a=-1/2sin2a
7)(cos29-cos91)/sin31=-2sin(-31)sin60/sin31=(2sin31*1/2)/sin31=1
8)cos75*cos15=1/2(cos60+cos90)=1/2*1/2=1/4