If `secalpha` and `cosecalpha` are the roots of the equation `x^2-px+q=0`, then (i)`p^2=q(q-2)` (ii)`p^2=q(q+2)` (iii)`p^2+q^2=2q` (iv) none of these

Options

A. `p^2=q(q-2)`
B. `p^2=q(q+2)`
C. `p^2+q^2=2q`
D. None of these

Answer

B

Explanation

`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`