Verified answer

3)

[tex]\displaystyle sin(\frac{3\pi }{2}+6\alpha )+cos(\pi -6\alpha )=-cos (6\alpha )-cos(6\alpha )=-2cos(6\alpha )[/tex]

4)

[tex]\displaystyle 2sin5\alpha *cos3\alpha -sin8\alpha =sin(5a+3a)+sin(5a-3a)-sin8\alpha =\\\\=sin8\alpha +sin2a-sin8\alpha =sin2\alpha[/tex]