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})$