Find the principal value of \({ tan }^{ -1 }\left( \frac { -1 }{ \sqrt { 3 } } \right) \)

Find the principal value of \({ cos }^{ -1 }\left( \frac { -1 }{ 2 } \right) \)

If \({ sin }^{ -1 }\left( \frac { 1 }{ 2 } \right) ={ tan }^{ -1 }x\) then find the value of x,

Evaluate \(sin\left( { cos }^{ -1 }\left( \frac { 3 }{ 5 } \right) \right) \)

Prove that \(2{ tan }^{ -1 }\left( \frac { 2 }{ 3 } \right) ={ tan }^{ -1 }\left( \frac { 12 }{ 5 } \right) \)