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 = _____________

(a)

\(sin2\alpha \)

(b)

\(sin\alpha \)

(c)

\(cos2\alpha \)

(d)

\(cos\alpha \)

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

(a)

0

(b)

\(\frac { 1 }{ 2 } \)

(c)

-1

(d)

none

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

(a)

\(\cfrac { \pi }{ 2 } \)

(b)

\(\cfrac { 5\pi }{ 3 } \)

(c)

\(\cfrac { 10\pi }{ 3 } \)

(d)

0

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

(a)

\(\cfrac { 1 }{ \sqrt { 2 } }

(b)

\(0\le x<\frac { 1 }{ \sqrt { 2 } } \)

(c)

\(-1\le x<\frac { 1 }{ \sqrt { 2 } } \)

(d)

x>0

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

(a)

0.75

(b)

1.5

(c)

0.96

(d)

sin^-1(1.5)