Question

If x.sin^3A+y.cos^3A=sinA.cosA
And x.sinA- y.cosA=0
Then prove 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, $x^2 + y^2 = Cos^2A + Sin^2A = 1$ 

Answer 2

here is your answer mate