Câu 3: C
Câu 6: D
ĐK: $cos\alpha \neq 0$
$tan\alpha + \frac{1}{tan\alpha}= 2$
$\Leftrightarrow tan^2\alpha -2tan\alpha + 1=0$
$\Leftrightarrow tan\alpha=1$
Câu 7: A
$(sin\alpha+cos\alpha)^2= m^2$
$\Leftrightarrow sin^2\alpha+cos^2\alpha + 2sin\alpha.cos\alpha = m^2$
$\Leftrightarrow sin\alpha.cos\alpha=\frac{m^2-1}{2}$
Câu 8: C
$sin(\frac{\pi}{2}-\alpha)= cos\alpha$
Câu 10: B
$= cos(\frac{\pi}{3}-\alpha)-cos(\alpha-\frac{2\pi}{3})$
$= cos\frac{\pi}{3}cos\alpha+sin\frac{\pi}{3}sin\alpha- cos\alpha.cos\frac{2\pi}{3} - sin\frac{2\pi}{3}sin\alpha$
Mà $cos\frac{2\pi}{3}= -cos\frac{\pi}{3}$
$sin\frac{2\pi}{3}= sin\frac{\pi}{3}$
$\Rightarrow M=2cos\alpha.cos\frac{\pi}{3}=2.\frac{1}{3}.\frac{1}{2}= \frac{1}{3}$
