a)\frac{1}{tan3a+tana}+\frac{1}{cot3a+cota}=cot4a b)cos3a.cos^{3}a+sin3a.sin^{3}a= cos^{3}2a c)cos^{2}(\alpha +\beta )+cos^{2}(\alpha -\beta )- cos2\alpha cos2\beta =1