Giải phương trình: cos5x + 2sinxcosx + 2sin3xsin2x = 0.

cos5x + 2sinxcosx + 2sin3xsin2x = 0

⇔ cos(3x+2x) + 2sinxcosx + 2sin3xsin2x = 0

⇔cos3xcos2x − sin3xsin2x + 2sinxcosx + 2sin3xsin2x = 0

⇔(cos3xcos2x + sin3xsin2x) + 2sinxcosx = 0

⇔ cos(3x−2x) + 2sinxcosx=0

⇔ cosx(1 + 2sinx) = 0

⇔ cosx=01+2sinx=0

⇔cosx=0sinx=−12

⇔x=kπ+π2x=−π6+k2πx=7π6+k2πk∈ℤ.