Hembek А)
Упростим числитель:
2*cos²α-1=2*cos²α-sin²α-cos²α=cos²α-sin²α=cos(2α).
Упростим знаменатель:
8*tg(π/4-α)*cos²(π/4-α)=8*(sin(π/4-α)/cos(π/4-α)*cos²(π/4-α)=
=8*sin(π/4-α)*cos(π/4-α)=4*sin(π/2-2α)=4*cos(2α).   ⇒
cos(2α)/(4*cos(2α))=1/4.



г) 4*sin⁴α+sin²(2α)-4*sin²α-7/2=4*sin²α*(sin²α-1)+sin²(2α)-7/2=
=4*sin²α*(-cos²α)+sin²(2α)-7/2=-(2*sinα*cosα)²+sin²(2α)-7/2=
=-sin²(2α)+sin²(2α)-7/2=-7/2.
Ответ: -7/2.

sangers1959

Verified answer

А)разбор по частям
1. 2cos²a-1=cos2a
2. 8tg(π/4-a)cos²(π/4-a)=8sin(π/4-a)   cos²(π/4-a)
                                        ⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻ *                      ⇒8sin(π/4-a)cos(π/4-a)
                                         cos(π/4-a)

4sin2(π/4-a)=4sin(π/2-2a)=4cos2a
3.cos2a/4cos2a=1/4=0.25


г)4sin⁴a+4sin²acos²a-4sin²a-7/2=4sin²a(sin²a+cos²a-1)-7/2=4sin²a(1-1)-7/2=4sin²a*0-7/2=0-7/2=-7/2=-3.5


в)расписываю первую часть
2(sin²a+cos²a)(sin⁴a-sin²acos²a+cos⁴a)=2*1*((sin²a+cos²a)²-2sin²acos²a-sin²acos²a)=
2(1-3sin²acos²a)=2-6sin²acos²a
 теперь вторая часть:
3((sin²a+cos²a)²-2cos²asin²a)=3(1-2sin²acos²a)=3-6sin²acos²a
 
итог
2-6sin²acos²a-(3-6sin²acos²a)=2-6sin²acos²a-3+6sin²acos²a=-1)))))