If x = sin2 θ cos θ and y = cos2 θ sin θ, then : (x2y)2/3 + (xy2)2/3 = - Maths - Trigonometry

Question

If x = sin2 θ cos θ and y = cos2
θ sin θ, then : (x2y)2/3 +
(xy2)2/3 = 1 
 x2 + y2 = x2y2 None of
these

Varun.Rawat · Accepted Answer

We have,x = sin2θ 
 cos θ; y = cos2θ 
 sin θNow, x2y = sin4θ 
 cos2θcos2θ 
 sin θ = sin3θNow, y2x = sin2θ 
 cos4θsin2θ 
 cos θ = cos3θLHS = x2y2/3 + y2x2/3=sin3θ2/3 + cos3θ2/3=sin2θ + cos2θ=1=RHS

If x = sin2 θ cos θ and y = cos2 θ sin θ, then : (x2y)2/3 + (xy2)2/3 = 1 x2 + y2 = x2y2 None of these

If x = sin² θ cos θ and y = cos² θ sin θ, then : (x²y)^2/3 + (xy²)^2/3 = 1 x² + y² = x²y² None of these