Question

if xsin³A+ycos³A=sinAcosA and xsinA=ycosA prove that x²+y²=1

Answer 1

Hey, that came in our school's mock test. Here what we'll do is - 

$(xsinA)(sin^{2}A) + ycos^{3}A = sinAcosA$
[tex]ycosA(sin^{2}A + cos^{2}A) = sinAcosA [/tex]
$y = sinA$

From second condition,

$xsinA = cosAsinA$
$x =  cosA$

$sin^2A + cos^2A = 1 =\ \textgreater \ x^2 + y^2 = 1$