Find the domain of sin⁻¹(2−3x²)

Find all the values of x such that -10\(\pi\)\(\le x\le\)10\(\pi\) and sin x = 0 

Find the domain of the following
 \(f\left( x \right) { =sin }^{ -1 }\left( \frac { { x }^{ 2 }+1 }{ 2x } \right) \)

Find the value of sin^-1\(\left( sin\frac { 5\pi }{ 9 } cos\frac { \pi }{ 9 } +cos\frac { 5\pi }{ 9 } sin\frac { \pi }{ 9 } \right) \).

Find the domain of cos^-1\((\frac{2+sinx}{3})\)

Find the value of
 \(cos\left( { cos }^{ -1 }\left( \frac { 4 }{ 5 } \right) +{ sin }^{ -1 }\left( \frac { 4 }{ 5 } \right) \right) \)

Find tan(tan^-1(2019))

Prove that tan (sin^-1x) = \(\frac{x}{\sqrt{1-x^{2}}} \), 1< x < 1

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

Show that cot⁻¹\(\left( \frac { 1 }{ \sqrt { { x }^{ 2 }-1 } } \right) ={ sec }^{ -1 }x,|x|>1\)

Simplify \({ cos }^{ -1 }\left( cos\left( \frac { 13\pi }{ 3 } \right) \right) \)

Evaluate \(sin\left[ { sin }^{ -1 }\left( \frac { 3 }{ 5 } \right) +{ sec }^{ -1 }\left( \frac { 5 }{ 4 } \right) \right] \)

If cos⁻¹ x + cos⁻¹ y + cos⁻¹  z = \(\pi \) and 0 < x, y, z < 1, show that x² + y² + z² + 2xyz = 1 

Solve \(cos\left( sin^{ -1 }\left( \frac { x }{ \sqrt { 1+{ x }^{ 2 } } } \right) \right) =sin\left\{ cot^{ -1 }\left( \frac { 3 }{ 4 } \right) \right\} \)

Find the value of the expression in terms of x, with the help of a reference triangle.
 sin(cos⁻¹(1-x))

Find the value of
\({ sin }^{ -1 }\left( cos\left( { sin }^{ -1 }\left( \frac { \sqrt { 3 } }{ 2 } \right) \right) \right) \)

Prove that 
\({ tan }^{ -1 }(\frac { 2 }{ 11 }) +{ tan }^{ -1 }(\frac { 7 }{ 24 }) ={ tan }^{ -1 }(\frac { 1 }{ 2 } )\)

Solve \({ sin }^{ -1 }\frac { 5 }{ x } +{ sin }^{ -1 }\frac { 12 }{ x } =\frac { \pi }{ 2 } \)

Find the domain of the following
g(x) = 2sin⁻¹(2x−1)−\(\frac{\pi}{4}\)

Find the value of \({ cos }^{ -1 }\left( cos\left( \frac { 4\pi }{ 3 } \right) \right) +{ cos }^{ -1 }\left( cos\left( \frac { 5\pi }{ 4 } \right) \right) \)

Find the value of
\(sin\left( { tan }^{ -1 }\left( \frac { 1 }{ 2 } \right) -{ cos }^{ -1 }\left( \frac { 4 }{ 5 } \right) \right) \)

Find the value of
\(cos\left( { sin }^{ -1 }\left( \frac { 4 }{ 5 } \right) -{ tan }^{ -1 }\left( \frac { 3 }{ 4 } \right) \right) \)

Find the value of the expression in terms of x, with the help of a reference triangle.
cos (tan^-1(3x-1))

Find the value of the expression in terms of x, with the help of a reference triangle.
tan\(\left( { sin }^{ -1 }\left( x+\frac { 1 }{ 2 } \right) \right) \)

Find the value of
\(cot\left( { sin }^{ -1 }\frac { 3 }{ 5 } +{ sin }^{ -1 }\frac { 4 }{ 5 } \right) \)

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

Prove that 
\({ sin }^{ -1 }(\frac { 3 }{ 5 } )-{ cos }^{ -1 (}\frac { 12 }{ 13 } )={ sin }^{ -1 }(\frac { 16 }{ 65 }) \)

Solve  \(2{ tan }^{ -1 }x={ cos }^{ -1 }\frac { 1-{ a }^{ 2 } }{ 1+{ a }^{ 2 } } -{ cos }^{ -1 }\frac { 1-{ b }^{ 2 } }{ 1+{ b }^{ 2 } } ,a>0,b>0\)

Solve \(2{ tan }^{ -1 }(cosx)={ tan }^{ -1 }(2cosec\ x)\)

Solve \({ cot }^{ -1 }x-{ cot }^{ -1 }\left( x+2 \right) =\frac { \pi }{ 12 } ,x>0\)

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

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

Simplify sin^-1[sin10]

Find all the values of x such that
\(-3 \pi \leq x \leq 3 \pi \text { and } \sin x=-1\)

Find tan⁻¹(\(-\sqrt3\))

Find tan⁻¹\((tan\frac{3\pi}{5})\)