Question

If x = a cos30°,y=b sin 30°, then
x^2/a^2 + y^2/b^2=
(A)a^2
(B)b^2
(C)1
(D)a^2+b^2
pls answer it soon
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Answer 1

Answer:

$x = a \: cos30 \\ \frac{x}{a} = cos30 = \frac{ \sqrt{3} }{2}$

$y = b \: sin30 \\ \frac{y}{b} = sin30 = \frac{1}{2}$

$now \\ \frac{ {x}^{2} }{ {a}^{2} } + \frac{ {y}^{2} }{ {b}^{2} } = {( \frac{ \sqrt{3} }{2} )}^{2} + {( \frac{1}{2} )}^{2} = \\ \frac{3}{4} + \frac{1}{4} = \frac{3 + 1}{4} = 1 \\ option \: c \: correct$

Answer 2

Step-by-step explanation:

$x = a \: cos30 \\ \frac{x}{a} = cos30 = \frac{ \sqrt{3} }{2}$

$y = b \: sin30 \\ \frac{y}{b} = sin30 = \frac{1}{2}$

$now \\ \frac{ {x}^{2} }{ {a}^{2} } + \frac{ {y}^{2} }{ {b}^{2} } = {( \frac{ \sqrt{3} }{2} )}^{2} + {( \frac{1}{2} )}^{2} = \\ \frac{3}{4} + \frac{1}{4} = \frac{3 + 1}{4} = 1 \\ option \: c \: correct$