Выражение: sin(19п/2+x)+cos(7п-x)+cos(7п/2-x)+sin(5п-x)

Sin(19π/2 + x) = sin(10π -  π/2 + x) = -sin(π/2 - x) = -cosx cos(7π - x) = cos(π - x) = -cosx cos(7π/2 - x) = cos(4π -  π/2 - x) = cos(π/2 + x) = -sinx sin(5π - x) = sin(π - x) = sinx -cosx - cosx - sinx + sinx = -2cosx

1)cos²a: (sin(a/2)/cos(a/2)-cos(a/2)/sin(a/2)=cos²a: (sin²(a/2)-cos²(a/2)/sin(a/2)cos(a/2)= cos²a: (-2cosa/sina)=-cos²a*sina/2cosa=-(sinacosa)/2=-sin2a/4 2)sin(a+π/4)/cos(a+π/4)-sin(a-π/4)/cos(a-π/4)=                                                (sin(a+π/4)cos(a-π/4)-sin(a-π/4)cos(a+π/4))/cos(a+π/4)cos(a-π/4)= (sin(a+π/4-a+π/4)): 1/2(cos(a+π/4-a+π/4)+cos(a+π/4+a-π/4)= sinπ/2: 1/2(cosπ/2+cos2a)=2/cos2a я решила 2 раза, если бы в примере стоял +,тогда получается 2tg2a.

Выражение: 2*(5-y^2)*(y^2+5)+(y^2-3)^2-(y^2+y-1)*(4-y^2) ответ: 63-11*y^2-y*4+y^3 решаем по шагам: 1. (10-2*y^2)*(y^2+5)+(y^2-3)^2-(y^2+y-1)*(4-y^2) 2. 50-2*y^4+(y^2-3)^2-(y^2+y-1)*(4-y^2) 3. 50-2*y^4+y^4-6*y^2+9-(y^2+y-1)*(4-y^2) 4. 50-y^4-6*y^2+9-(y^2+y-1)*(4-y^2) 5. 59-y^4-6*y^2-(y^2+y-1)*(4-y^2) 6. 59-y^4-6*y^2-(5*y^2-y^4+y*4-y^3-4) 7. 59-y^4-6*y^2-5*y^2+y^4-y*4+y^3+4 8. 59-y^4-11*y^2+y^4-y*4+y^3+4 9. 59-11*y^2-y*4+y^3+4 10. 63-11*y^2-y*4+y^3 решаем по действиям: 1. 2*(5-y^2)=10-2*y^2 2. (10-2*y^2)*(y^2+5)=50-2*y^4 3. (y^2-3)^2=y^4-6*y^2+9 4. -2*y^4+y^4=-1*y^4 5. 50+9=59 6. (y^2+y-1)*(4-y^2)=5*y^2-y^4+y*4-y^3-4 7. 59-y^4-6*y^2-(5*y^2-y^4+y*4-y^3-4)=59-y^4-6*y^2-5*y^2+y^4-y*4+y^3+4 8. -6*y^2-5*y^2=-11*y^2 9. -y^4+y^4=0 10. 59+4=63