Question

((sina+sin3a)/(cosa+cos3a))*(1 - cos4a)

Answer 1

$\displaystyle\frac{sina+sin3a}{cosa+cos3a}*(1-cos4a)= \frac{2sin\frac{a+3a}{2}*cos \frac{a-3a}{2}}{+2cos\frac{a+3a}{2}*cos\frac{a-3a}{2}}*(1-(2cos^22a-1))=\\\\= \frac{2sin(2a)*cosa}{2cos2a*cosa}*(-2cos^22a)= \frac{sin2a}{cos2a}*(-2cos^22a)=\\\\=-2sin2a*cos2a=-sin4a$