Question

(4sin^2 2a)-(8sin^4 a)+(8sin^2 a) найдите значение выражения

Answer 1

4(1-cos4a)/2-8(1-cos2a)²/4+8(1-cos2a)/2=
=2(1-cos4a)-2(1-cos2a)²+4(1-cos2a)=
=2-2cos4a-2+4cos2a-2cos²2a+4-4cos2a=
=-2cos4a-2cos²2a+4=-2cos4a-2(1+cos4a)/2+4=
=-2cos4a-1-cos4a+4=3-3cos4a=3(1-cos4a)=3*2sin²2a=6sin²2a