if tan^-1 (a/x) + tan^-1 (b/x) = \(\pi\) /2, then x = 

2

(a)

\(\sqrt { ab } \)

if (a < 0) and x \(\varepsilon \) (-a, a), simplify tan^-1 \(\left( \frac { x }{ \sqrt { { a }^{ 2 }-{ x }^{ 2 } } } \right) \)

2

(a)

\(-sin^{ -1 }\left( \frac { x }{ a } \right) \)

If x + y + z = xyz , then the valu of tan^-1x + tan^-1y + tan^-1 z =

2

(a)

\(\pi\)

Write in the simplest form : \({ tan }^{ -1 }\left[ \frac { cos\quad x }{ 1+sin\quad x } \right] ,x\left[ -\frac { \pi }{ 2 } ,\frac { \pi }{ 2 } \right] \)

2

(a)

Write in the simplest form: \(({ tan }^{ -1 }\left[ \frac { \sqrt { 1+sin\quad x } +{ \sqrt { 1-sin\quad x } }\quad }{ \sqrt { 1+sin\quad x } +{ \sqrt { 1-sin\quad x } } } \right] ,0<x<\frac { \pi }{ 2 } \)

2

(a)

Show that : \({ sin }^{ -1 }\frac { 5 }{ 13 } +{ cos }^{ -1 }\frac { 3 }{ 5 } ={ tan }^{ -1 }\frac { 63 }{ 16 } \)

2

(a)

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

2

(a)

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

2

(a)

Find the value of \(\tan \left(\sin ^{-1} \frac{3}{5}+\cot ^{-1} \frac{3}{2}\right)\)

4

(a)

Does the following trigonometric equation have any solutions? If yes, obtain the solutions (s);
\(tan^{ -1 }\left( \frac { x+1 }{ x-1 } \right) +tan^{ -1 }\left( \frac { x-1 }{ x } \right) =-tan^{ -1 }7\)

4

(a)