1.

If x = a cos3 θ and y = b sin3 θ, then the value of \(\bigg(\frac{x}{a}\bigg)^\frac23 +\bigg(\frac{y}{b}\bigg)^\frac23\) is(a) 1 (b) –2 (c) 2 (d) –1

Answer»

(a) 1

\(\bigg(\frac{x}{a}\bigg)^\frac23 +\bigg(\frac{y}{b}\bigg)^\frac23\) = \(\bigg(\sqrt[3]{\frac{a\,cos^3\,\theta}{a}}\bigg)^2 + \bigg(\sqrt[3]\frac{b\,sin^3\,\theta}{b}\bigg)^2\)

= (sin θ)2 + (cos θ)2 = sin2 θ + cos2 θ = 1



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