Question

Demonstrati ca :
cos^2012 55° - sin^2012 35° = 0
sin² 20° + sin² 70° = 1

Answer 1

[tex]a) \\ cos^{_{2012}}55^o - sin^{_{2012}}55^o= \\ =(cos~55^o )^{2012} - (sin~35^o)^{2012} = \\ =(sin(90^o-55^o) )^{2012} - (sin~35^o)^{2012} = \\ =(sin~35^o )^{2012} - (sin~35^o)^{2012} = \boxed{0}~~~cctd\\ \\ b) \\ sin^2\,20^o + sin^2\,70^o = \\ =sin^2\,20^o + cos^2\,(90^o-70^o) = \\ =sin^2\,20^o + cos^2\,(20^o) = \boxed{1}~~~cctd[/tex]