sin 5x + sin x + 2 cos^2 x = 1 ____________________________________

Question

sin 5x + sin x + 2 cos^2 x = 1

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Answer 1

2sin(3x)*cos (2x)+2(1-cos(2x))/2=1. 2sin(3x)*cos(2x)+1-cos(2x)=1 . cos(2x)=1.  cos(2x)(2sin/3x)-1)=0.   2sin(3x)-1=0.  2x=n/2+ni.   x=n/4+n/2.   sin(3x)=1/2.   3x=(-1)*n/6+nm.     x=(-1)*n/18+nm/3