CMR a) cot ² a – cos ² a = cot ² a . cos ² a b) $\frac{1 + cos a }{sin a}$ = $\frac{sin a}{1 – cos a}$

a) $\cot^2a – \cos^2a$

$= \dfrac{\cos^2a}{\sin^2a} – \cos^2a$

$= \dfrac{\cos^2a – \sin^2a.\cos^2a}{\sin^2a}$

$= \dfrac{\cos^2a(1 – \sin^2a)}{\sin^2a}$

$= \dfrac{\cos^2a.\cos^2a}{\sin^2a}$

$= \cot^2a.\cos^2a$

b) $\dfrac{1 + \cos a}{\sin a} = \dfrac{\sin a}{1 – \cos a}$

$\to (1 + \cos a)(1 – \cos a) = \sin^2a$

$\to 1 – \cos^2a = \sin^2a$

$\to \sin^2a = \sin^2a$ (hiển nhiên)

Vậy $\dfrac{1 + \cos a}{\sin a} = \dfrac{\sin a}{1 – \cos a}$