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)

\(x-\pi\)

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

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

The domain of the function defined by \(f(x)=\sin ^{-1} \sqrt{x-1}\) is

(a)

[1, 2]

(b)

[-1, 1]

(c)

[0, 1]

(d)

[-1, 0]

\(\sin ^{-1}\left(\tan \frac{\pi}{4}\right)-\sin ^{-1}\left(\sqrt{\frac{3}{x}}\right)=\frac{\pi}{6}\). Then x is a root of the equation

(a)

x²−x−6 = 0

(b)

x²−x−12 = 0

(c)

x²+x−12 = 0

(d)

x²+x−6 = 0

sin (tan^-1x), |x| < 1 is equal to

(a)

\(\frac{x}{\sqrt{1-x^2}}\)

(b)

\(\frac{1}{\sqrt{1-x^2}}\)

(c)

\(\frac{1}{\sqrt{1+x^2}}\)

(d)

\(\frac{x}{\sqrt{1+x^2}}\)

Amplitude of sine function

(1)

cosec^-1x

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

(2)

does not exist

cos^-1(-x)

(3)

1

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

(4)

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

\({ sec }^{ -1 }(2)\)

(5)

\(\pi \)

Find the principal value of sin^-1(2), if it exists.

For what value of x does sinx = sin⁻¹x?

State the reason for cos^-1\([cos(-\frac{\pi}{6})]\neq \frac{\pi}{6}.\)

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

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

Find the period and amplitude of y = 4sin(−2x)

Find the value of 
tan (tan⁻¹(1947))

Simplify sin^-1[sin10]

Find the domain of sin⁻¹(2−3x²)

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

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

Find the principal value of cos⁻¹\(\left( \frac { \sqrt { 3 } }{ 2 } \right) \)

Solve \(tan^{ -1 }\left( \frac { x-1 }{ x-2 } \right) +tan^{ -1 }\left( \frac { x+1 }{ x+2 } \right) =\frac { \pi }{ 4 } \)

Find the principal value of
sec⁻¹(−2).