A) sin^2(π/2 + t) + sin^2(π – t) = cos^2t + sin^2t = 1
<span>б) cos(π/2-t)ctg(-t) / sin(π/2+t) =(sint)*(cost/sint) / cost = 1</span>
Первое понятно, остальные не очень
1.2i-3/1+i=(-3+2i)/(1+i)=(-3*1+2*1)/(1²+1²)+(1*2-(-3)*1)/(1²+1²)*i=-1/2+5/2*i= -0,5+2,5i
2. i^3=i²*i=-1i=-i [i^4=i²*i²=-1*(-1)=1] i^7=i^4*i^3=1*(-i)=-i i^32=i^4*8=1
i^31=i^4*7 *i^31*(-1)=-1
i^65=i^(4*16+1)=1*i=i i^-15=i^15=i^(4*3)*i^3=1*(-1)=-1 i^45 =i^(4*11+1)=1*i=i
i^28=i^4*7=1
1).25а^3 - аb^2 = a(25a^2 - b^2) = a(5a-b)(5a+b)
2).-3х^2 - 12х-12 = -3(x^2 + 4x + 4) = -3(x+2)^2
3).3ab-15a+12b-60 = 3a(b-5) + 12(b-5) = (b-5)(3a+12)
4).a^4 - 625
= a^4 - 5^4 = (a^2)^2 - (5^2)^2 = (a^2 - 5^2)(a^2+5^2)