Giải thích các bước giải:
c.$\sin^4a(1+2\cos^2a)+\cos^4a(1+2\sin^2a)$
$=\sin^4a(1+2\cos^2a)+\cos^4a(1+2\sin^2a)$
$=\sin^4a+2\sin^4a\cos^2a+\cos^4a+2\cos^4a\sin^2a$
$=\sin^4a+\cos^4a+2\sin^4a\cos^2a+2\cos^4a\sin^2a$
$=\sin^4a+\cos^4a+2\sin^2a\cos^2a(\sin^2a+\cos^2a)$
$=\sin^4a+\cos^4a+2\sin^2a\cos^2a$
$=(\sin^2a+\cos^2a)^2$
$=1$
d.$\dfrac{\cos^2a-\cot^2a}{\sin^2a-\tan^2a}$
$=\dfrac{\cos^2a-\dfrac{\cos^2a}{\sin^2a}}{\sin^2a-\dfrac{\sin^2a}{\cos^2a}}$
$=\dfrac{\cos^2a(1-\dfrac{1}{\sin^2a})}{\sin^2a(1-\dfrac{1}{\cos^2a})}$
$=\dfrac{\cos^2a.\dfrac{\sin^2a-1}{\sin^2a}}{\sin^2a.\dfrac{\cos^2a-1}{\cos^2a}}$
$=\dfrac{\cos^2a.\dfrac{-\cos^2a}{\sin^2a}}{\sin^2a.\dfrac{-\sin^2a}{\cos^2a}}$
$=\dfrac{\cos^6a}{\sin^6a}$
$=\cot^6a$
