Question

Biết tan\(\alpha=3.\) Tính M =\(\frac{\sin\alpha.\cos\alpha}{\sin^2\alpha-\cos^2\alpha}\)

Answer 1

Lời giải:

$\tan a=3\neq 0$ nên $\sin a, \cos a\neq 0$

$\frac{1}{M}=\frac{\sin ^2a-\cos ^2a}{\sin a\cos a}=\frac{\sin a}{\cos a}-\frac{\cos a}{\sin a}$

$=\tan a-\frac{1}{\tan a}=3-\frac{1}{3}=\frac{8}{3}$