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: Option 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