If $\frac{x}{3}=2 \sin A, \frac{y}{3}=2 \cos A$, then the value of $x^{2}+y^{2}$ is :\

Question

Professor PC Thomas Classes · Answer

(a): We have, $\frac{x}{3}=2 \sin A \Rightarrow x=6 \sin A$\ and $\frac{y}{3}=2 \cos A \Rightarrow y=6 \cos A$\ Now, $x^{2}+y^{2}=(6 \sin A)^{2}+(6 \cos A)^{2}$\ $=36 \sin ^{2} A+36 \cos ^{2} A$\ $=36\left(\sin ^{2} A+\cos ^{2} Aight)=36(1)$\ ( $\because \sin ^{2} 	heta+\cos ^{2} 	heta=1$ )\ $=36$\