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Solution: We have
L.H.S. = Cos(3π/4+x)-cos(3π/4-x)
= cos 3π/4 cos x - sin 3π/4 sin x - [cos 3π/4 cos x + sin 3π/4 sin x]
= cos 3π/4 cos x - sin 3π/4 sin x - cos 3π/4 cos x - sin 3π/4 sin x]
= -2sin 3π/4 sin x
= -2 x (1/√2) sin x
= -√2sin x
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