I f xsin^3 \theta+ycos^3 θ= sin θcosθand x sin θ=ycosθ, sin θ≠0, cosθ≠0,thenx^2 + y^2 is

RRB NTPC Mains or Stage 2 Model Paper 3 with solutions

Question : 7 of 120

Marks: +1, -0

I f

xsin^3 θ+ycos^3

θ= sin θcosθand x sin θ=ycosθ, sin θ≠0, cosθ≠0,then

x^2 + y^2

Solution:

x sin^3 θ + y cos^3 θ= sin θ. cos θ

(x sin θ) sin^2 θ + (y cos θ) cos^2 θ = sin θ cos θ

∴ x sin θ= y cos θ

∴ x sin θ (sin^2 θ+ cos^2 θ) = sin θ cos θ

x = cos θ

x sin θ = y cos θ

y = sin θ

so x^2 + y^2 = sin^2 θ + cos^2 θ= 1

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