If #xsin^3theta+ycos^3theta= sinthetacostheta and xsintheta=ycostheta#, thenprove that #x^2 +y^2 =1#?

1 Answer
Apr 29, 2018

Given

#xsin^3theta+ycos^3theta= sinthetacostheta and xsintheta=ycostheta#

So

#xsin^3theta+ycos^3theta= sinthetacostheta#

#=>ycosthetasin^2theta+ycos^3theta= sinthetacostheta#

#=>ycostheta(sin^2theta+cos^2theta)= sinthetacostheta#

#=>ycosthetaxx1= sinthetacostheta#

#=y=sintheta#

Again

#xsintheta=ycostheta#

#=>xsintheta=sinthetaxxcostheta#

#=>x=costheta#

Hence

#x^2+y^2=cos^2theta+sin^2theta=1#