State the reason for cos^-1\([cos(-\frac{\pi}{6})]\neq \frac{\pi}{6}.\)

Is cos^-1(-x) = \(\pi\)-cos⁻¹(x) true? Justify your answer.

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

Find the value of sec⁻¹\(\left( -\frac { 2\sqrt { 3 } }{ 3 } \right) \)

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

Find the value of  \({ tan }^{ -1 }\left( \sqrt { 3 } \right) -{ sec }^{ -1 }(-2)\)

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

Find the value of 
tan (tan⁻¹(1947))

Simplify sin^-1[sin10]

Find the value of \(cos\left[ \frac { 1 }{ 2 } { cos }^{ -1 }\left( \frac { 1 }{ 8 } \right) \right] \) 

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

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

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