Find the principal value of sin^-1(2), if it exists.

Find the period and amplitude of y = sin 7x

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

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

Prove that \(\frac{\pi}{2}\le sin^{-1}x+2 cos^{-1} x\le\frac{3\pi}{2}\)

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

Prove that tan^-1 x + tan^-1 z = tan^-1\(\left[ \frac { x+y+z-xyz }{ 1-xy-yz-zx } \right] \)

Find the value of \({ cos }^{ -1 }\left( cos\frac { \pi }{ 7 } cos\frac { \pi }{ 17 } -sin\frac { \pi }{ 7 } sin\frac { \pi }{ 17 } \right) .\)

Find the principal value of
cot^-1 \((\sqrt{3})\)

Simplify \({ sec }^{ -1 }\left( sec\left( \frac { 5\pi }{ 3 } \right) \right) \)

Simplify sin^-1[sin10]

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

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

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

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