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If pcos e ctheta+qcottheta=2 and p^2cos ...

If `pcos e ctheta+qcottheta=2` and `p^2cos e c^2theta-q^2theta=5` then the value of `sqrt(81 p^(-2))` is________

Text Solution

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The correct Answer is:
16
We have `p cosec theta+qcottheta=2 …(1)`
`And (pcosectheta)^2-(qcottheta)^2=5`
`rArr pcosectheta-qcottheta=5/2 ...(2)`
Form (1) and (2)
`pcosectheta=9/4,qcot theta=(-1)/4`
Now, `cosec^2theta-cot^2theta=1`
`rArr 81/(16p^2)-1/(16p^2)=1`
`rArr 81p^(-2)-q^(-2)=16`
`rArr sqrt(81p^(-2)-q^(-2))=4`
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