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.
2x+1+3x=11
5x+1=11
5x=10
X=2
Cos(π/4-t)=cos(π/2-(π/4+t))=sin(π/4+t)
cos(5π/12+t)=cos(π/2-(π/12-t))=sin(π/12-t)
------------------------------
cos(π/4+t)cos(π/12-t)-sin(π/4+t)sin(π/12-t)=cos(π/4+t+π/12-t)=
=cosπ/3=1/2
log25(9) - log5(3) = 1/2*2*log5(3) - log5(3) = 0
Решение смотри на фотографии