Giải thích các bước giải:
$\dfrac{tan^2a-tan^2b}{tan^2a.tan^2b}\\ \\
=\dfrac{\frac{sin^2a}{cos^2a}-\dfrac{sin^2b}{cos^2b}}{\dfrac{sin^2a}{cos^2a}.\dfrac{sin^2b}{cos^2b}}\\ \\
= \dfrac{\dfrac{sin^2a.cos^2b}{cos^2a.cos^2b}-\dfrac{sin^2b.cos^2a}{cos^2b.cos^2a}}{\dfrac{sin^2a}{cos^2a}.\dfrac{sin^2b}{cos^2b}}\\ \\
= \dfrac{\dfrac{sin^2a.cos^2b-sin^2b.cos^2a}{cos^2a.cos^2b}}{\dfrac{sin^2a.sin^2b}{cos^2a.cos^2b}}\\ \\
= \dfrac{sin^2a.cos^2b-sin^2b.cos^2a}{cos^2a.cos^2b.\dfrac{sin^2a.sin^2b}{cos^2a.cos^2b}}\\ \\
= \dfrac{sin^2a.cos^2b-sin^2b.cos^2a}{sin^2a.sin^2b}\\ \\
=\dfrac{sin^2a.(1-sin^2b)-sin^2b.(1-sin^2a)}{sin^2a.sin^2b}\\ \\
=\dfrac{sin^2a-sin^2asin^2b-sin^2b+sin^2bsin^2a}{sin^2a.sin^2b}\\ \\
=\dfrac{sin^2a-sin^2b}{sin^2a.sin^2b}$
