If x sin³A + y cos³A = sinA cosA and x sinA = y cosA, prove that x²+y² = 1 .
Answers
Answered by
18
xsin^3 A+ycos^3 A=sinA cosA xsinA=ycosA......(1)
or xsin^2 A× sinA+ycos^3A=sinA cosA
or ycosA.sin^2 A +ycos^3A =sinA cosA
or ycos A (sin^2 A +cos^2 A)=sinA cosA
So y=sinA
So x=cosA(using (1) )
So x^2+y^2=sin^2 A+ cos^2 A=1
Hence proved
or xsin^2 A× sinA+ycos^3A=sinA cosA
or ycosA.sin^2 A +ycos^3A =sinA cosA
or ycos A (sin^2 A +cos^2 A)=sinA cosA
So y=sinA
So x=cosA(using (1) )
So x^2+y^2=sin^2 A+ cos^2 A=1
Hence proved
Similar questions