If $xsin^3θ+ycos^3θ = sinθ cosθ$ and $x sinθ = y cos θ$, then the value of $x^2 + y^2$ is :
Answer & explanation
Correct answer: option 3
Given :-
x sin³θ + y cos³θ = sinθ.cosθ---(1)
and xsinθ = ycosθ ---(2)
ycosθ. sin²θ + y cos³θ = sinθ.cosθ
ycosθ. ( sin²θ + cos²θ ) = sinθ.cosθ
{ Using sin²θ + cos²θ = 1 }
y = sinθ
Putting value of y in equation 2.
xsinθ = sinθ. cosθ
x = cosθ
x² + y² = sin²θ + cos²θ = 1