Question

Упростите выражение
1) 0,125cos4a+sin^2acos^2a
2) sin^2ytgy-cos^2yctgy+2ctg2y
3)1+cos421-cos42

Answer 1

1) 1/8cos4α+sin²αcos²α=1/8cos4α+1/4sin²2α=1/8cos²2α-1/8sin²2α+1/4sin²2α=
=1/8cos²2α+1/8sin²2α=1/8(cos²2α+sin²2α)=1/8*1=1/8;
2) sin²ytgy-cos²yctgy+2ctg2y=sin²y*siny/cosy-cos²y*cosy/siny+2ctg2y=
=(sin^4y-cos^4y)/(sinycosy)+2ctg2y=
=(sin²y-cos²y)(sin²y+cos²y)/(1/2sin2y)+2ctg2y=-2cos2y/sin2y+2ctg2y=
=-2ctg2y+2ctg2y=0; 
3)(1+cos42°)/(1-cos42°)=ctg²21.