Question

упростите выражение ....

Answer 1

1)=sina+sin5a-sin3a=sina+2*sina*cos4a=
sina(1+2cos4a)=sina(1+2((2cos²2a)-1)=
sina(1+4cos²2a-2)=sina(4cos²2a-1)=
sina((2cos2a-1)(2cos2a+1)
2)sina(2cos2a+1)=sina(2cos²a-2sin²a+
sin²a+cos²a)=sina(3cos²a-sin²a)=
sina(3-3sin²a-sin²a)=3sina-4sin³a=
sin3a

Answer 2

$frac{sin(5pi -alpha )+cos(frac{5pi}{2}-5alpha )+sin(3alpha -pi )}{2cos2alpha-1} =frac{sin(pi -alpha )+cos(frac{pi}{2}-5alpha )-sin(pi-3alpha )}{2cos2alpha-1} =$$=frac{sinalpha+sin5alpha -sin3alpha}{2cos2alpha-1} = frac{2sin3alpha*cos2alpha -sin3alpha}{2cos2alpha-1} =frac{sin3alpha(2cos2alpha -1)}{2cos2alpha-1} = sin3alpha$