a) $\tan^2\alpha - \sin^2\alpha.\tan^2\alpha + \cos^2\alpha$
$= \tan^2\alpha(1 - \sin^2\alpha) +\cos^2\alpha$
$= \tan^2\alpha.\cos^2\alpha + \cos^2\alpha$
$=\dfrac{\sin^2\alpha}{\cos^2\alpha}\cos^2\alpha + \cos^2\alpha$
$= \sin^2\alpha + \cos^2\alpha = 1$
b) $\cos^280^o - \cos^270^o + \cos^260^o +\cos^30^o - \cos^20^o + \cos^10^o$
$= \cos^280^o - \cos^270^o + \cos^260^o + \sin^260^o - \sin^270^o + \sin^280^o$
$= (\cos^280^o + \sin^280^o) - (\cos^270^o + \sin^270^o) + (\cos^260^o + \sin^260^o)$
$= 1 - 1 + 1 = 1$
