JAMB - Mathematics (2006 - No. 13)
Differentiate (cos θ - sin θ)\(^2\)
-2 cos 2θ
-2 sin2θ
1 - 2 cos 2θ
1 - 2 sin 2θ
설명
y = (cosθ - sinθ)
dy/dx = 2(cosθ - sinθ)(-sinθ - cosθ)
dy/dx = 2(-cosθsinθ - cos2θ + sin2θ)
dy/dx = 2(- cos\(^2\)θ + sin\(^2\)θ)
= -2(cos\(^2\)θ - sin\(^2\)θ)
= -2(1 - 2sin\(^2\)θ)
= -2cos2θ