Q. Which one of following is true?
A) $\sin{\left( \cos^{- 1}x \right) = \cos{(\sin^{- 1}x)}}$
B) $\sec{\left( tan^{- 1}x \right) = \tan{(\sec^{- 1}x)}}$
C) $\cos{\left( \tan^{- 1}x \right) = \tan{(\cos^{- 1}x)}}$
D) $\tan{\left( \sin^{- 1}x \right) = \sin{(\tan^{- 1}x)}}$
Explanation
(a)
$\sin{\left( \cos^{- 1}x \right) = \cos{(\sin^{- 1}x)}}$
$\Rightarrow \ \ \sin{\left( \frac{\pi}{2} - \sin^{- 1}x \right) = \cos{(\sin^{- 1}x)}}$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sin^{- 1}{x = \sin^{- 1}x}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.