Differentiate (cos \theta - sin \theta)\(^2\)
A
-2 cos 2θ
B
-2 sin2θ
C
1 - 2 cos 2θ
D
1 - 2 sin 2θ
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
y = (cos\theta - sin\theta)
dy/dx = 2(cos\theta - sin\theta)(-sin\theta - cos\theta)
dy/dx = 2(-cos\thetasin\theta - cos2\theta + sin2\theta)
dy/dx = 2(- cos\(^2\)\theta + sin\(^2\)\theta)
= -2(cos\(^2\)\theta - sin\(^2\)\theta)
= -2(1 - 2sin\(^2\)\theta)
= -2cos2\theta
Source: Myschool Past Questions Archive (Record #8727)