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

If \(\sin ^{-1} \frac{x}{5}+\operatorname{cosec}^{-1} \frac{5}{4}=\frac{\pi}{2}\), then the value of x is

If \(\sin ^{-1} x+\cot ^{-1}\left(\frac{1}{2}\right)=\frac{\pi}{2}\), then x is equal to

The equation \(\tan ^{-1} x-\cot ^{-1} x=\tan ^{-1}\left(\frac{1}{\sqrt{3}}\right)\)has

If |x| \(\le\) 1, then 2 tan^-1 x-sin^-1\(\frac{2x}{1+x^2}\) is equal to

If \(\cot ^{-1}(\sqrt{\sin \alpha})+\tan ^{-1}(\sqrt{\sin \alpha})=u\), then cos2u is equal to

sin^-1(2cos²x-1)+cos^-1(1-2sin²x)=

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

If cot^-1 2 and cot^-1 3 are two angles of a triangle, then the third angle is

If the function f(x) = sin^-1(x² - 3), then x belongs to

\(\tan ^{-1}\left(\frac{1}{4}\right)+\tan ^{-1}\left(\frac{2}{9}\right)\) is equal to

If \(x = \frac{1}{5}\), the value of cos (cos^-1x+2sin^-1x) is

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

If \(\cot ^{-1} x=\frac{2 \pi}{5}\) for some x \(\in\) R, the value of tan^-1 x is

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

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

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

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

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

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