The value of sin^-1 (cos x), \(0\le x\le\pi\) is

(a)

\(\pi-x\)

(b)

\(x-\frac{\pi}{2}\)

(c)

\(\frac{\pi}{2}-x\)

(d)

\(x-\pi\)

\(\sin ^{-1} \frac{3}{5}-\cos ^{-1} \frac{12}{13}+\sec ^{-1} \frac{5}{3}-\operatorname{cosec}^{-1} \frac{13}{12}\) is equal to

(a)

2\(\pi\)

(b)

\(\pi\)

(c)

0

(d)

tan^-1\(\frac{12}{65}\)

If sin^-1 x+sin^-1 y+sin^-1 \(z = \frac{3\pi}{2}\), the value of x²⁰¹⁷+y²⁰¹⁸+z²⁰¹⁹\(-\frac { 9 }{ { x }^{ 101 }+{ y }^{ 101 }+{ z }^{ 101 } } \)is

(a)

0

(b)

1

(c)

2

(d)

3

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

(a)

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

(b)

\(\frac { \sqrt { 3 } }{ 2 } \)

(c)

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

(d)

none of these

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

(a)

2

(b)

3

(c)

1

(d)

none

cos^-1(4x³-3x)

(1)

3cos^-1x

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

(2)

\(\frac { \pi }{ 2 } \)

cos^-1(-x)

(3)

\(\frac { 4 }{ 5 } \)

\({ sec }^{ -1 }\left( \frac { 2 }{ 3 } \right) +{ cosec }^{ -1 }\left( \frac { 2 }{ 3 } \right) \)

(4)

cosec^-1x

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

(5)

\(\pi -{ cos }^{ -1 }x\)