Cos (450 - θ) - sin (450 + θ) =
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written in reverse for my convenience
= - sin (45 + θ) + cos (45 - θ)
= - (sin 45.cos θ + cos 45.sin θ) +( cos 45.cos θ + sin 45.sin θ )
=- sin 45.cos θ - cos 45.sin θ + cos 45.cos θ + sin 45.sin θ
= - (sin 45.cos θ - sin 45.sin θ) - (cos 45.sin θ - cos 45.cos θ)
= - sin 45(cos θ - sin θ) + cos 45(cos θ - sin θ)
= (cos 45 - sin 45) (cos θ - sin θ)
= 0 (cos θ - sin θ)
= 0 .....
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