\({ tan }^{ -1 }\left( tan\cfrac { 9\pi }{ 8 } \right) \)

The pricipal value of \({ sin }^{ -1 }\left( \frac { -1 }{ 2 } \right) \) is _________

If x < 0, y < 0 such that xy = 1, then tan^-1(x) + tan^-1(y) =_____

The value of \({ sin }^{ -1 }\left( cos\frac { 33\pi }{ 5 } \right) \) is________

If \(\theta ={ sin }^{ -1 }\left( sin(-{ 60 }^{ 0 }) \right) \) then one of the possible values of \(\theta\) is _________

If x > 1, then \(2{ tan }^{ -1 }x+{ sin }^{ -1 }\left( \frac { 2x }{ 1+{ x }^{ 2 } } \right) \) ________

The value of sin 2(tan^-1 0.75) is ___________

The value of tan \(\left( { cos }^{ -1 }\frac { 3 }{ 5 } +{ tan }^{ -1 }\frac { 1 }{ 4 } \right) \) is ______

The domain of cos^-1(x² - 4) is______

If tan^-1(cot \(\theta\)) = 2\(\theta\), then\(\theta\) = _____________

\(cot\left( \frac { \pi }{ 4 } -{ cot }^{ -1 }3 \right) \)

In a \(\Delta ABC\)  if C is a right angle, then  \({ tan }^{ -1 }\left( \frac { a }{ b+c } \right) +{ tan }^{ -1 }\left( \frac { b }{ c+a } \right) =\) ________

If \({ cos }^{ -1 }x>x>{ sin }^{ -1 }x\) then _________

If \({ tan }^{ -1 }\left( \frac { x+1 }{ x-1 } \right) +{ tan }^{ -1 }\left( \frac { x-1 }{ x } \right) ={ tan }^{ -1 }\left( -7 \right) \) then x is ___________

If \(4{ cos }^{ -1 }x+{ sin }^{ -1 }x=\pi \) then x is _____________

\(sin\left\{ 2{ cos }^{ -1 }\left( \frac { -3 }{ 5 } \right) \right\} =\) __________

The value of \({ cos }^{ -1 }\left( \cos\cfrac { 5\pi }{ 3 } \right) +sin^{ -1 }\left( \sin\cfrac{5\pi }{ 3 } \right) \) is ______________ 

If tan^-1(3) + tan^-1(x) = tan^-1(8) then x = ____________ 

\({ tan }^{ -1 }\left( \frac { 1 }{ 4 } \right) +{ tan }^{ -1 }\left( \frac { 2 }{ 11 } \right) \) = ____________

If \(\alpha ={ tan }^{ -1 }\left( \frac { \sqrt { 3 } }{ 2y-x } \right) ,\beta ={ tan }^{ -1 }\left( \frac { 2x-y }{ \sqrt { 3y } } \right) \) then \(\alpha -\beta \) __________

If \(\alpha ={ tan }^{ -1 }\left( tan\frac { 5\pi }{ 4 } \right) \) and \(\beta ={ tan }^{ -1 }\left( -tan\frac { 2\pi }{ 3 } \right) \) then ___________

The number of solutions of the equation \({ tan }^{ -1 }2x+{ tan }^{ -1 }3x=\frac { \pi }{ 4 } \) ____________

If \({ sin }^{ -1 }x-cos^{ -1 }x=\frac { \pi }{ 6 } \) then ___________

If \({ tan }^{ -1 }\left\{ \cfrac { \sqrt { 1+{ x }^{ 2 } } -\sqrt { 1-{ x }^{ 2 } } }{ \sqrt { 1+{ x }^{ 2 } } +\sqrt { 1-{ x }^{ 2 } } } \right\} =\alpha \) then x² = _____________