Statement-1 : ^ - 1 [ ( e/ x^2 ) ( e x^2 ) ] + ^ - 1 [ (e x^2 ) (… - Vidyadip

MCQ

Statement-$1$ : ${\cot ^{ - 1}}\left[ {\frac{{\log \left( {e/{x^2}} \right)}}{{\log \left( {e{x^2}} \right)}}} \right] + {\cot ^{ - 1}}\left[ {\frac{{\log (e{x^2})}}{{\log (e/{x^2})}}} \right]$ = $\frac {\pi}{2}$

Statement-$2$ : ${\tan ^{ - 1}}\left[ {\frac{{1 + \log {x^2}}}{{1 - \log {x^2}}}} \right]$ = ${\tan ^{ - 1}}\,1 + \,{\tan ^{ - 1}}\left( {\log {x^2}} \right)$

A
Statement-$1$ is true, Statement-$2$ is true;Statement-$2$ is not the correct explanation of Statement-$1$ .
B
Statement-$1$ is false, Statement-$2$ is true.
C
Statement-$1$ is true, Statement-$2$ is false
✓
Statement-$1$ is true, Statement-$2$ is true;Statement-$2$ is the correct explanation of Statement-$1$ .

✓

Answer

Correct option: D.

Statement-$1$ is true, Statement-$2$ is true;Statement-$2$ is the correct explanation of Statement-$1$ .

d

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