Q. If we consider only the principle value of the inverse trigonometric functions, then the value of $\tan\left( \cos^{- 1}{\frac{1}{5\sqrt{2}} - \sin^{- 1}\frac{4}{\sqrt{17}}} \right)$ is
A) $\sqrt{\frac{29}{3}}$
B) $\frac{29}{3}$
C) $\sqrt{\frac{3}{29}}$
D) $\frac{3}{29}$
Explanation
(d)
$\tan\left( \cos^{- 1}{\frac{1}{5\sqrt{2}} - \sin^{- 1}\frac{4}{\sqrt{17}}} \right)$
$= \tan{(\tan^{- 1}{7 - \tan^{- 1}{4)}}}$
$= \tan\left\lbrack \tan^{- 1}\left( \frac{7 - 4}{1 + 28} \right) \right\rbrack = \frac{3}{29}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.