Đáp án:
Giải thích các bước giải:
$cos5x - sin3x = \sqrt{3}(cos3x - sin5x)$
$<+> cos 5x - \sqrt{3}.cos3x = sin3x - \sqrt{3}.sin5x $
$<=> \frac{1}{2} .cos5x - \frac{\sqrt{3}}{2}.cos3x = \frac{1}{2}.sin3x - \frac{\sqrt{3}}{2}.sin5x$
$<=> \frac{1}{2} .cos5x+ \frac{\sqrt{3}}{2}.sin5x = \frac{\sqrt{3}}{2}.cos3x+ \frac{1}{2}.sin3x$
$<=> sin(\frac{π}{6} + 5x) = sin(\frac{π}{3} + 3x) $
<=> \(\left[ \begin{array}{l}\frac{π}{6} + 5x =\frac{π}{3} + 3x + k2 π\\\frac{π}{6} + 5x= \frac{2}{3}π-3x + k2π\end{array} \right.\) <=> \(\left[ \begin{array}{l}x=\frac{π}{12}+ kπ\\x=\frac{π}{16}+ \frac{kπ}{4}\end{array} \right.\) (k ∈Z)
b)