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

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Solution

Q.
$I f \frac{x}{3} = 2 s i n A, \frac{y}{3} = 2 c o s A, t h e n t h e v a l u e o f x^{2} + y^{2} i s$

1 36

2 9

3 6

4 18

Ans.
(1)

$G i v e n, \frac{x}{3} = 2 s i n A \Rightarrow s i n A = \frac{x}{6} a n d \frac{y}{3} = 2 c o s A \Rightarrow c o s A = \frac{y}{6} W e k n o w t h a t {s i n}^{2} A + {c o s}^{2} A = 1 \Rightarrow \frac{x^{2}}{36} + \frac{y^{2}}{36} = 1 \Rightarrow x^{2} + y^{2} = 36$

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