If x sin3 θ + y cos3 θ = sin θ cos θ and x sin θ − y cos θ = 0 , then the value of x2 + y2 equals
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Correct answer: A
Explanation
The correct option is 1.
x sin3 θ + y cos3 θ = sin θ cos θ --> eq 1
x sin θ − y cos θ = 0
x sin θ = y cos θ --->eq2
substituting in eq1
y cos θ sin2 θ + y cos3 θ = sin θ cos θ
taking y cos θ common
y cos θ(sin2 θ + cos2 θ) = sin θ cos θ { we know sin2 θ + cos2 θ = 1}
y cos θ = sin θ cos θ
y = sin θ
substituting in eq 2
x sin θ = sin θ cos θ
x = cos θ
x2 + y2 = sin2 θ + cos2 θ = 1