Question

1. (cos^2a-sin^2a)^2-4sin^2a*cos^2a 2. 1-cos a/sin a/4*cos a/4

Answer 1

1) $(cos^{2}a-sin^{2}a)^{2}-4sin^{2}a*cos^{2}a=cos^{2}(2a)-(2sina*cosa)^{2}=$$=cos^{2}(2a)-sin^{2}(2a)=cos(2*2a)=cos(4a)$

2) $\frac{1-cosa}{sin(\frac{a}{4})*cos(\frac{a}{4})}=\frac{1-cosa}{0.5*sin(\frac{a}{2})}=\frac{2*(1-cosa)}{sin(\frac{a}{2})}=$$=\frac{2*(1-cosa)}{sin(\frac{a}{2})}=\frac{2*2* \frac{(1-cosa)}{2}}{sin(\frac{a}{2})}=\frac{4sin^{2}(\frac{a}{2})}{sin(\frac{a}{2})}=4sin(\frac{a}{2})$