Question

If xsin^3 A + ycos^3 A = sinAcosA and xsin A - ycos A = 0 than prove that, x^2 + y^2 = 1​

Answer 1

Given xSinA – yCosA = 0

⇒ x.SinA = y CosA     ........(1)

Consider xSin^3A+yCos^3A = SinACosA

xSin^3A+yCosACos^2A = SinACosA

xSin^3A+ xSinACos^2A = SinACosA     {From eq 1}

xSin^3A+ xSinA(1-Sin^2A) = SinACosA

xSin^3A+ xSinA-xSin^3A = SinACosA

xSinA = SinACosA

x = CosA          ......(2)

Substitute this value in the eq (1)

We get y = SinA

so, x^2 + y^2 = Cos^2A + Sin^2A = 1  

Hope this helps u