Q. If $\theta\$and$\ \phi$ are the roots of the equation $8x^{2} + 22x + 5 = 0,$ then
A) Both $\sin^{- 1}\theta$ and $\sin^{- 1}\phi$ are equal
B) Both $\sec^{- 1}\theta$ and $\sec^{- 1}\phi$ are equal
C) Both $\tan^{- 1}\theta$ and $\tan^{- 1}\phi$ are equal
D) None of the above
Explanation
(c)
$8x^{2} + 22x + 5 = 0 \Rightarrow x = - \frac{1}{4}, - \frac{5}{2}$
$\therefore - 1 < - \frac{1}{4} < 1\ and - \frac{5}{2} < - 1$
$\therefore\sin^{- 1}\left( - \frac{1}{4} \right)$ exists but $\sin^{- 1}\left( - \frac{5}{2} \right)$ does not exist.
$\sec^{- 1}{\left( - \frac{5}{2} \right)exists}$ but $\sec^{- 1}\left( - \frac{1}{4} \right)$does not exist.
$\tan^{- 1}\left( - \frac{1}{4} \right)$ and $\tan^{- 1}\left( - \frac{5}{2} \right)$ both exist.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.