If x=acos3θ and y=asin3θ, 1+(dy/dx)2 is equal to:
tanθ
tan2θ
1
sec2θ
Explanation for the correct option.
Step 1: Differentiate xandy w.r.t θ
x=acos3θ⇒dxdθ=-3acos2θsinθ
y=asin3θ⇒dydθ=3asin2θcosθ
Step 2: Find dydx
dydx=dydθ×dθdx=3asin2θcosθ-3acos2θsinθ=-tanθ
Step 3: Find 1+(dy/dx)2
1+(dy/dx)2=1+-tanθ2=sec2θ
Hence, option D is correct.
find (d2y/dx2)if x=a(theta+sin(theta))
,y=a(1-cos(theta))