Find the value of \({\cot ^{ - 1}}\left( {\frac{4}{5}} \right) + {\co

1.	Find the value of \({\cot ^{ - 1}}\left( {\frac{4}{5}} \right) + {\cot ^{ - 1}}\left( { - \frac{4}{5}} \right)\).
Answer» Correct Answer - Option 3 : π Concept: It is known that \({\cot ^{ - 1}}\left( { - x} \right) = \pi - {\cot ^{ - 1}}\left( x \right)\) for all value \(x \in R\). Calculation: The expression be rewritten as \({\cot ^{ - 1}}\left( {\frac{4}{5}} \right) + {\cot ^{ - 1}}\left( { - \frac{4}{5}} \right)\) \(= {\cot ^{ - 1}}\left( {4/5} \right) + \left( {\pi - {{\cot }^{ - 1}}\left( {4/5} \right)} \right)\) \(= {\cot ^{ - 1}}\left( {4/5} \right) + \pi - {\cot ^{ - 1}}\left( {4/5} \right)\) \(= \pi\)

Find the value of \({\cot ^{ - 1}}\left( {\frac{4}{5}} \right) + {\cot ^{ - 1}}\left( { - \frac{4}{5}} \right)\).

Answer» Correct Answer - Option 3 : π

Concept:

It is known that \({\cot ^{ - 1}}\left( { - x} \right) = \pi - {\cot ^{ - 1}}\left( x \right)\) for all value \(x \in R\).

Calculation:

The expression be rewritten as \({\cot ^{ - 1}}\left( {\frac{4}{5}} \right) + {\cot ^{ - 1}}\left( { - \frac{4}{5}} \right)\)

\(= {\cot ^{ - 1}}\left( {4/5} \right) + \left( {\pi - {{\cot }^{ - 1}}\left( {4/5} \right)} \right)\)

\(= {\cot ^{ - 1}}\left( {4/5} \right) + \pi - {\cot ^{ - 1}}\left( {4/5} \right)\)

\(= \pi\)