5. cos2x + 2cosx = 2$sin^{2}$$\frac{x}{2}$
⇔ cos2x + 2cosx - 1 = -1 + 2$sin^{2}$$\frac{x}{2}$
⇔ cos2x + 2cosx - 1 = - cosx
⇔ cos2x + 2cosx - 1 + cosx = 0
⇔ cos2x + 3cosx = 1
⇔ 2$cos^{2}$x - 1 + 3cosx = 1
⇔ 2$cos^{2}$x + 3cosx - 2 = 0
⇔ \(\left[ \begin{array}{l}cosx = \frac{1}{2}\\cos x = -2\end{array} \right.\)
⇔ x = ± $\frac{x}{3}$ + 2k$\pi$ ( k ∈ Z )
7. 3$sin^{2}$x - 2sin2x + 6$cos^{2}$x = 2 ( cosx $\neq$ 0 ⇔ x $\neq$ $\frac{\pi}{2}$ + k $\pi$ )
⇔ 3$sin^{2}$x - 4sinxcosx + 5$cos^{2}$x = 2
⇔ 3$tan^{2}$x - 4tanx + 5 - 2 = 0
⇔ 3$tan^{2}$x - 4tanx + 3 = 0
⇔ \(\left[ \begin{array}{l}x = \frac{\pi}{4} + k\pi\\arctan -3 + k\pi\end{array} \right.\)
