Question #0d91d

2 Answers
Jun 17, 2016

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).

Jun 17, 2016

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)