Question

If x=rcos theta and y = r sin theta then show thay xsquare + ysquare = R square.​

Answer 1

$\pink{\bold{ANSWER}}$

$\rm{x^2\:+y^2\:=R^2}$

$\red{\bold{EXPLANATION}}$

$\rm{x=Cos\theta}$

$\underline{SQUARING\:ON\:BOTH\:SIDES\:WE\:HAVE}$

$\rm{x^2=Cos^2\theta}$ ...$\rm{Equation\:01}$

$\rm{y=Sin\theta}$

$\underline{SQUARING\:ON\:BOTH\:SIDES\:WE\:HAVE}$

$\rm{y^2=Sin^2\theta}$ ...$\rm{Equation\:02}$

$\mathbb{ADD\:BOTH\:THE\: EQUATIONS\:WE\:HAVE}$

$\rm{x^2\:+\:y^2\:=R^2Sin^2\theta\:+R^2Cos^2\theta}$

$\rm{x^2\:+\:y^2\:=R^2\left(Sin^2\theta\:+Cos^2\theta\right)}$

$\rm{x^2\:+\:y^2\:=R^2}$

$\boxed{\rm{Becoz\:Sin^2\theta\:+Cos^2\theta\:=1}}$

$\therefore$ $\rm{x^2\:+y^2\:=R^2}$