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Which of the following is not the quadra...

Which of the following is not the quadratic equation whose roots are `cosec^2thetaand sec^2theta`?

A

`x^2-6x+6=0`

B

`x^2-7x+7=0`

C

`x^2-4x+4=0`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
D
`sec^2theta+cosec^2theta=1/cos^2theta+1/sin^2theta`
`=(cos^2theta+sin^2theta)/(cos^2thetasin^2theta)=sec^2thetacosec^2theta`
Now, `sec^2theta+cosec^2theta=2+tan^2theta+cot^2theta`
`=4+(tantheta-cottheta)^2`
`ge4`
Hence, all equations can have roots `sec^2theta" and " cosec^2theta`.
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