| Assertion [A]: The value of \[\cos \left( {{\sec }^{-1}}\left( \frac{5}{3} \right) \right)\] is, \[\frac{3}{5}\]. |
| Reason [R]: Value of \[{{\sec }^{-1}}x\] is \[{{\cos }^{-1}}\frac{1}{x}\]. |
A) Both A and R are individually true and R is the correct explanation of A.
B) Both A and R are individually true and R is not the correct explanation of A.
C) 'A' is true but 'R' is false
D) 'A' is false but 'R' is true
E) Both A and R are false.
Correct Answer: A
Solution :
\[\cos \left( {{\sec }^{-1}}\left( \frac{5}{3} \right) \right)=\cos \left( {{\cos }^{-1}}\left( \frac{3}{5} \right) \right)=\frac{3}{5}\] Here both statement are true and Reason R is the correct explanation of Assertion A. \[\therefore \]Option [A] is the correct answer.
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