Question

Assertion :${\text{cosec}}^{-1}\left(3/2\right)+{\cos }^{-1}\left(2/3\right)-2{\cot }^{-1}\left(1/7\right)-{\cot }^{-1}7$ is equal to ${\cot }^{-1}7$ Reason: ${\sin }^{-1}x+{\cos }^{-1}x=\pi /2,{\tan }^{-1}x+{\cot }^{-1}x=\pi /2,{\text{cosec}}^{-1}x={\sin }^{-1}\left(1/x\right),$

${\cot }^{-1}\left(1/x\right)={\tan }^{-1}\left(x\right),{\cot }^{-1}\left(x\right)={\tan }^{-1}\left(1/x\right)$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is D Assertion is incorrect but Reason is correct

Reason is true
Assertion:
$cose{c}^{-1}\frac{3}{2}+{\cos }^{-1}\frac{2}{3}-2{\cot }^{-1}\frac{1}{7}-{\cot }^{-1}7={\sin }^{-1}\frac{2}{3}+{\cos }^{-1}\frac{2}{3}-({\tan }^{-1}7+{\cot }^{-1}7)-{\cot }^{-1}\frac{1}{7}=\frac{\pi }{2}-\frac{\pi }{2}-{\cot }^{-1}\frac{1}{7}=-{\tan }^{-1}7$
Hence, assertion is wrong