Question

50 баллов ТРИГОНОМЕТРИЯ, СРОЧНО
УПРОСТИТЬ ВЫРАЖЕНИЕ
sin^2((pi/2)+А)-cos^4(pi-A)+cos^4((3pi/2)-A)

Answer 1

sin((pi/2)+А) = cos(А)
cos(pi-A) = -cos(A)
cos((3pi/2)-A) = -sin(A)
... = cos^2(А) - cos^4(А) + sin^4(A) =
= cos^2(A) + (sin^2(A) - cos^2(A))(sin^2(A) + cos^2(A)) =
= cos^2(A) + sin^2(A) - cos^2(A) = sin^2(A)

Answer 2

$=cos^2 \alpha -cos^4 \alpha +sin^4 \alpha =cos^2 \alpha -(cos^4 \alpha -sin^4 \alpha)=$$cos^2 \alpha -(cos^2 \alpha -sin^2 \alpha)(cos^2 \alpha +sin^2 \alpha)=cos^2 \alpha -cos^2 \alpha +sin^2 \alpha=sin^2 \alpha$