Which of the following pairs may represent the eccentricities of two conjugate hyperbolas, for `alpha in (0,pi//2)`?
a.`sin theta, cos theta` b.`tan theta, cot theta` c.`sec theta, "cosec"theta` d.`1+sintheta,1+cos theta`

Options

A. `sin theta, cos theta`
B. `tan theta, cot theta`
C. `sec theta, "cosec"theta`
D. `1+sintheta,1+cos theta`

Answer

C

Explanation

If `e_(1)` and `e_(2)` are the eccentricities of two conjugate hyperbolas, then
`(1)/(e_(1)^(2))+(1)/(e_(2)^(2))=1`
Therefore, `e_(1)=sec theta and e_(2)="cosec"theta.`