Question #0d91d

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Question #0d91d

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Answer 1 · 2016-06-17T14:40:51

$y= (3/4)(2-x^2).$

Explanation:

Recall the identity : $sin^2theta=(1-cos2theta)/2.$

Hence,
$y=3sin^2theta=(3/2)(1-cos2theta).$ ..............(1)

But, it is given that $x=sqrt(2cos2theta),$
so that $x^2/2=cos2theta.$

Now, putting this value of $cos2theta$ in (1), we get,

$y= (3/2)(1-x^2/2)=(3/4)(2-x^2).$

Answer 2 · 2016-06-17T15:08:39

$y=(x^2-2)/-2$

Explanation:

$y=3sin^2theta$
$x=sqrt(2cos2theta)$
$x^2=2cos2theta$
= $2cos^2theta-2sin^2theta$
= $2cos^2theta-2/3y$
= $2(1-1/3y)-2/3y$
= $2-4/3y$
so
$y=-3/4(x^2-2)$

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Question #0d91d

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