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)

\(x-\pi\)

If \(\sin ^{-1} x+\sin ^{-1} y=\frac{2 \pi}{3}\); then cos^-1 x + cos^-1 y is equal to

(a)

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

(b)

\(\frac{\pi}{3}\)

(c)

\(\frac{\pi}{6}\)

(d)

\(\pi\)

If sin⁻¹x = 2sin⁻¹ \(\alpha\) has a solution, then

(a)

\(|\alpha |\le \frac { 1 }{ \sqrt { 2 } } \)

(b)

\(|\alpha |\ge \frac { 1 }{ \sqrt { 2 } } \)

(c)

\(|\alpha |<\frac { 1 }{ \sqrt { 2 } } \)

(d)

\(|\alpha |>\frac { 1 }{ \sqrt { 2 } } \)

\(\sin ^{-1}(\cos x)=\frac{\pi}{2}-x\) is valid for

(a)

\(-\pi \le x\le 0\)

(b)

\(0 \le x\le \pi\)

(c)

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

(d)

\(-\frac { \pi }{ 4 } \le x\le \frac { 3\pi }{ 4 } \)

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