If x sin3θ + y cos3θ = sinθcosθ, and x sinθ - y cosθ = 0, then find the value of (x2 + y2).
Answer & explanation
Correct answer: option 4
x sin3θ + y cos3θ = sinθcosθ ----(i)
& x sinθ - y cosθ = 0 ⇒ x sinθ = ycosθ ----- (ii)
in eqn (i)
y cosθ.sin2θ + ycosθ.cos2θ = sinθcosθ
y cosθ (sin2θ + cos2θ) = sinθcosθ
y = sinθ
from eqn (ii) x = cosθ
∴ x2 + y2 = sin2θ + cos2θ = 1