a,
$VT= 2(\sin^6a+\cos^6a)+1$
$=2(\sin^a+\cos^2a)(\sin^4a-\sin^2a.\cos^2a+\cos^4a)+1$
$= 2\sin^4a-2\sin^2a\cos^2a+2\cos^4a+1$
$= 2\sin^4a+2\cos^4a+(1-2\sin^2a\cos^2a)$
$VP=3(\sin^4a+\cos^4a)$
$=2\sin^4a+2\cos^4a+\sin^4a+\cos^4a$
$= 2\sin^4a+2\cos^4a+(\sin^2a+\cos^2a)-2\sin^2a.\cos^2a$
$= 2\sin^4a+2\cos^4a+1-2\sin^2a\cos^2a= VT$ (đpcm)
b,
$VT=\dfrac{\tan a-\tan b}{\cot a-\cot b}$
$=\dfrac{\frac{\sin a.\cos b -\cos a.\sin b}{\cos a.\cos b}}{\frac{\cos a.\sin b-\sin a.\cos b}{\sin a.\sin b}}$
$=\dfrac{\sin(a-b)}{\cos a.\cos b} : \dfrac{\sin(b-a)}{\sin a.\sin b}$
$=\dfrac{\sin(a-b)}{\cos a.\cos b}. \dfrac{\sin a.\sin b}{-\sin(a-b)}$
$=-\tan a.\tan b$
