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If 2sin^2theta=3\ costheta,\ w h e r e\ ...

If `2sin^2theta=3\ costheta,\ w h e r e\ 0lt=thetalt=2pi,` then find the value of `thetadot`

A

`(2pi)/(3),(5pi)/(3)`

B

`(pi)/(3),(5pi)/(3)`

C

`(5)/(3),(4pi)/(3)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Given, `2sin^(2)theta=3costheta`
`therefore2(1-cos^(2)theta)=3costheta`
`rArr2cos^(2)theta+3costheta-2=0`
`rArr(costheta+2)(2costheta-1)=0`
`rArrcostheta=-2orcostheta=(1)/(2)`
But `costhetain[-1,1]`
`therefore " "costhetane-2`
Now, `costheta=(1)/(2)`
`costheta="cos"(pi)/(3)`
As `thetain[0,2pi]`
`thereforetheta=(pi)/(3),(5pi)/(3)`
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