Differentiate cos - sin 2 - JAMB Mathematics 2006 Question
Differentiate (cos θ - sin θ)2
A
-2 cos 2θ
B
-2 sin2θ
C
1 - 2 cos 2θ
D
1 - 2 sin 2θ
correct option: a
y = (cosθ - sinθ)
dy/dx = 2(cosθ - sinθ)(-sinθ - cosθ)
dy/dx = 2(-cosθsinθ - cos2θ + sin2θ)
dy/dx = 2(- cos2θ + sin2θ)
= -2(cos2θ - sin2θ)
= -2(1 - sin2θ)
= -2cos2θ
dy/dx = 2(cosθ - sinθ)(-sinθ - cosθ)
dy/dx = 2(-cosθsinθ - cos2θ + sin2θ)
dy/dx = 2(- cos2θ + sin2θ)
= -2(cos2θ - sin2θ)
= -2(1 - sin2θ)
= -2cos2θ
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