∵sin(2x+ φ )= sinφcos2x+cosφsin2x
sin(-2x+ φ )=sinφcos2x-cosφsin2x
∵sin(-2x+ φ )=sin(2x+ φ )
∴sinφcos2x+cosφsin2x=sinφcos2x-cosφsin2x
∵sin(2x+ φ )= sinφcos2x+cosφsin2x
sin(-2x+ φ )=sinφcos2x-cosφsin2x
∵sin(-2x+ φ )=sin(2x+ φ )
∴sinφcos2x+cosφsin2x=sinφcos2x-cosφsin2x