Differentiate (cos θ – sin θ)\(^2\)
-
-2 cos 2θ
- -2 sin2θ
- 1 - 2 cos 2θ
- 1 - 2 sin 2θ
The correct answer is: A
Explanation
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