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Prove that cos(3π/4+x)-cos(3π/4-x) = -√2sin x

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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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