2006
Mathematics
JAMB
Differentiate (cos θ - sin θ)2
A.
-2 cos 2θ
B.
-2 sin2θ
C.
1 - 2 cos 2θ
D.
1 - 2 sin 2θ
Correct Answer: -2 cos 2θ
Explanation
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
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) = -2cos2θTHIS WEEK's
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