Question

If a cos³θ + 3a cosθ sin²θ = x and a sin³θ + 3a cos²θ sinθ = y, then (x + y)^2/3 + (x − y)^2/3 =

(A)  2a^2/3 

(B)  a^2/3 

(C)  3a^2/3 

(D)  2a^1/3

Answer 1

Correct option (A)  2a^2/3 

a cos³θ + 3a cosθ sin² θ = x

a sin³ θ + 3a cos² θ sin θ = y

x + y = a[sin³θ + cos³θ + 3 sinθ cosθ (sinθ + cosθ)]

= a(sinθ + cosθ)³

(x + y/a)^1/3 = sinθ + cosθ  ....(i)

 – y = a[cos³ θ – sin³θ + 3 cosθ sin²θ – 3 cos² θ sin θ] = a[cosθ – sinθ]³

(x - y)^1/3 = cosθ - sinθ ......(2)