Inverse Trigono...

If \(tan^{-1}\) x + \(tan^{-1}\)y = \(\frac{4\pi}{5}\), then \(cot^{-1} \)x + \(cot^{-1} \)y equals to

If \(sin^{-1}\)\((\frac{2a}{1+a^2})\) + \(cos^{-1}\)\((\frac{1-a^2}{1+a^2})\) = \(tan^{-1}\)\((\frac{2x}{1-x^2})\), where a, x \(\in\) [0,1) then the value of x is

The value of the expression tan(\(\frac{1}{2}\)\(cos^{-1}\)\(\frac{2}{\sqrt5}\)) is

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

If \(cos^{-1 }\)\(\alpha\) + \(cos^{-1 }\)\(\beta\) + \(cos^{-1 }\)\(\gamma\) = 3\(\pi\), then \(\alpha\)(\(\beta\) + \(\gamma\)) + \(\beta\)(\(\gamma\) + \(\alpha\)) + \(\gamma\)(\(\alpha\) + \(\beta\)) equals

The number of real Solution of the equation \(\sqrt{1+cos2x}\) = \(\sqrt2\)\(cos^{-1}\) (cos x) in \([\frac{\pi}{2},\pi]\) is

The principal value of \(sin^{-1}\)\((-\frac{1}{2})\) is

1 + \(cot^2\)\((sin^{-1}x)\) =