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(5\pi -\alpha )+cos(\frac{5\pi}{2}-5\alpha )+sin(3\alpha -\pi )}{2cos2\alpha-1} =\frac{sin(\pi -\alpha )+cos(\frac{\pi}{2}-5\alpha )-sin(\pi-3\alpha )}{2cos2\alpha-1} =$$=\frac{sin\alpha+sin5\alpha -sin3\alpha}{2cos2\alpha-1} = \frac{2sin3\alpha*cos2\alpha -sin3\alpha}{2cos2\alpha-1} =\frac{sin3\alpha(2cos2\alpha -1)}{2cos2\alpha-1} = sin3\alpha$