The value of $$\tan \left( {2{{\tan }^{ - 1}}{1 \over 5} - {\pi \over 4}} \right)$$ is

Consider the following statements

1. $${\sin ^{ - 1}}{4 \over 5} + {\sin ^{ - 1}}{3 \over 5} = {\pi \over 2}$$

2. $${\tan ^{ - 1}}\sqrt 3 + {\tan ^{ - 1}}1 = - {\tan ^{ - 1}}(2 + \sqrt 3 )$$

Which of the above statement(s) is/are correct?

Consider the following statements

1. Theer exists $$\theta \in \left( { - {\pi \over 2},{\pi \over 2}} \right)$$ for which $${\tan ^{ - 1}}(\tan \theta ) \ne 0$$.

2. $${\sin ^{ - 1}}\left( {{1 \over 3}} \right) - {\sin ^{ - 1}}\left( {{1 \over 5}} \right)$$

$$ = {\sin ^{ - 1}}\left( {{{2\sqrt 2 (\sqrt 3 - 1)} \over {15}}} \right)$$

Which of the above statements is/are correct?

Consider the following statements

1. $${\tan ^{ - 1}}x + {\tan ^{ - 1}}\left( {{1 \over x}} \right) = \pi $$

2. Their exist, $$x,y \in [ - 1,1]$$, where x $$\ne$$ y such that $${\sin ^{ - 1}}x + {\cos ^{ - 1}}y = {\pi \over 2}$$.

Which of the above statements is/are correct?