A) 1
B) 2
C) 3
D) 4
Correct Answer: A
Solution :
Key Idea: \[{{\sin }^{-1}}x+{{\cos }^{-1}}x=\frac{\pi }{2}\] and \[{{\tan }^{-1}}x+{{\cot }^{-1}}x=\frac{\pi }{2}\] \[\sin \left( {{\sin }^{-1}}\frac{1}{3}+{{\sec }^{-1}}3 \right)\]\[+\cos \left( {{\tan }^{-1}}\frac{1}{2}+{{\tan }^{-1}}2 \right)\] \[=\sin \left( {{\sin }^{-1}}\frac{1}{3}+{{\cos }^{-1}}\frac{1}{3} \right)\] \[+\cos \left( {{\tan }^{-1}}\frac{1}{2}+{{\cot }^{-1}}\frac{1}{2} \right)\] \[=\sin \left( \frac{\pi }{2} \right)+\cos \left( \frac{\pi }{2} \right)=1\]
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