Find all the values of x such that
 -3\(\pi\)\(\le x\le\)-3\(\pi\) and sin x = -1

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

Find the principal value of sin^-1(-1).

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

If \({ cot }^{ -1 }\left( \frac { 1 }{ 7 } \right) =\theta \) find the value of cos \(\theta \)

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

Prove that \({ tan }^{ -1 }\left( \frac { 1 }{ 7 } \right) +{ tan }^{ -1 }\left( \frac { 1 }{ 13 } \right) ={ tan }^{ -1 }\left( \frac { 2 }{ 9 } \right) \)

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

Evaluate \(sin\left( \frac { 1 }{ 2 } { cos }^{ -1 }\frac { 4 }{ 5 } \right) \)

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

Evaluate \(sin\left( { cos }^{ -1 }\left( \frac { 1 }{ 2 } \right) \right) \)

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

Find the principal value of \(\operatorname{cosec}^{-1}(-\sqrt{2})\)

Find the value of \(\cos ^{-1}\left(\cos \frac{13 \pi}{6}\right)\)

Find the value of \(\sin \left(\frac{\pi}{3}+\cos ^{-1}\left(-\frac{1}{2}\right)\right)\)