Questions in inv-trig

Select	Question
	If ${{\cos }^{-1}}\sqrt{p}+{{\cos }^{-1}}\sqrt{1-p}+{{\cos }^{-1}}\sqrt{1-q}=\frac{3\pi }{4},$ then the value of q is
	${{\cot }^{-1}}[{{(\cos \alpha )}^{1/2}}]-{{\tan }^{-1}}[{{(\cos \alpha )}^{1/2}}]=x,$then $\sin x=$
	If ${{\tan }^{-1}}x+{{\tan }^{-1}}y+{{\tan }^{-1}}z=\pi ,$ then $\frac{1}{xy}+\frac{1}{yz}+\frac{1}{zx}=$
	$\tan \left[ \frac{1}{2}{{\sin }^{-1}}\left( \frac{2a}{1+{{a}^{2}}} \right)+\frac{1}{2}{{\cos }^{-1}}\left( \frac{1-{{a}^{2}}}{1+{{a}^{2}}} \right) \right]=$
	If $A={{\tan }^{-1}}x$, then $\sin 2A=$
	If $\cos (2{{\sin }^{-1}}x)=\frac{1}{9},$then $x=$
	If $2{{\tan }^{-1}}(\cos x)={{\tan }^{-1}}(2\text{cosec }x),$ then x =
	$\tan \left( 2{{\cos }^{-1}}\frac{3}{5} \right)=$
	$\tan \left[ 2{{\tan }^{-1}}\left( \frac{1}{5} \right)-\frac{\pi }{4} \right]=$
	If $2{{\cos }^{-1}}\sqrt{\frac{1+x}{2}}=\frac{\pi }{2},$then $x=$