`cos 7x+sin 8x=cos 3x-sin 2x`
`<=>sin 8x+sin 2x=cos 3x-cos 7x`
`<=>2sin 5x cos 2x=2sin 2x sin 5x`
`<=>sin 5x(cos 2x-sin 2x)=0`
`<=>sin 5x cos (2x+\pi/4)=0`
`<=>[(sin 5x=0),(cos (2x+\pi/4)=0):}`
`<=>[(5x=k\pi),(2x+\pi/4=\pi/2+k\pi):}`
`<=>[(x=k\pi/5),(x=\pi/8+k\pi/2):}` `(k in ZZ)`