If the points `(1,1):(0,sec^2theta);` and `(cos e c^2theta,0)` are collinear, then find the value of `theta`

Answer

`theta=R-{(npi)/(2),ninZ}`

Explanation

The given points are collinear.
`therefore" "(1)/(2)|{:(1,,,1),(0,,,sec^2theta),(cosec^2theta,,,0),(1,,,1):}|=0`
`rArrsec^2theta-cosec^2theta sec^2theta+ cosec^2theta=0`
`rArr(1)/(cos^2theta)-(1)/(sin^2thetacos^2theta)+(1)/(sin^2theta)=theta`
`rArr(1)/(sin^2thetacos^2theta)-(1)/(sin^2thetacos^2theta)=theta`
Therefore,the points are collinear for all value of `theta`, expect only `theta=(npi)/(2),nin Z`.
Thus, `thetain R-{(npi)/(2),nin Z}`