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If sec `alphaa n dalpha` are the roots of `x^2-p x+q+0,` then `p^2=q(q-2)` (b) `p^2=q(q+2)` `p^2q^2=2q` (d) none of these

A

`p^2=q(q-2)`

B

`p^2=q(q+2)`

C

`p^2+q^2=2q`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`secalpha+cosecalpha=p,secalphacosecalpha=q`
`or (sinalpha+cosalpha)/(sinalphacosalpha)=p" and" 1/(sinalphacosalpha)=q`
`or (1+2sinalpha+cosalpha)/(sin^2alphacos^2alpha)=p^2`
`or (1+2/q)/(1/q^2)=p^2`
`or q^2(1+2/q)=p^2orq(q+2)=p^2`
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