7. Giải các phương trình sau: a)sin3x -cos5x=0                     b) tan3xtanx=1.

Giải:

a) sin3x - cos5x = 0$\iff \sin 3x = \cos 5x \iff \cos 5x=\cos \left(\frac{\mathrm{\pi }}{2}-3x\right)$

$\iff {[}_{5x=-\frac{\mathrm{\pi }}{2}+3x+k2\mathrm{\pi }}^{5x=\frac{\mathrm{\pi }}{2}-3x+k2\mathrm{\pi }}\iff {[}_{2x = -\frac{\mathrm{\pi }}{2}+k2\mathrm{\pi }}^{8x=\frac{\mathrm{\pi }}{2}+k2\mathrm{\pi }}\iff {[}_{x=-\frac{\mathrm{\pi }}{4}+k\mathrm{\pi }}^{x = \frac{\mathrm{\pi }}{16}+k\frac{\mathrm{\pi }}{4}} (k\in \mathrm{\mathbb{Z}})$

b) Điều kiện: cos3x ≠0; cosx≠0

tan3xtanx = 1 $\iff \tan 3x = \frac{1}{\tan x}\iff \tan 3x=cotx\iff \tan 3x=\tan (\frac{\mathrm{\pi }}{2}-x)$

                        $\iff 3x = \frac{\mathrm{\pi }}{2}-x+k\mathrm{\pi }\iff \mathrm{x}=\frac{\mathrm{\pi }}{8}+\mathrm{k}\frac{\mathrm{\pi }}{4}, \mathrm{k}\in \mathrm{\mathbb{Z}}$