Mathematics

Differentiate (cos θ – sin θ)(^2)

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