Question

( tan left(cos ^{-1} xright)=sin left(tan ^{-1} 2right) )
( tan left(tan ^{-1} frac{sqrt{1-x^{2}}}{x}right)=sin left(sin ^{-1} frac{2}{sqrt{5}}right) quad frac{1}{sqrt{5}} x )
( frac{sqrt{1-x^{2}}}{x}=frac{2}{sqrt{5}}left(begin{array}{l}text { squaring } text { both sides }end{array}right) )
( pi )
( frac{1-x^{2}}{x^{2}}=frac{4}{5} )
( 5-5 x^{2}=4 x^{2} )
( 5=9 x^{2} quadleft[text { Any } x=frac{3}{sqrt{5}}right] )
( x=sqrt{frac{9}{5}} )

# (1) tan (cos-1 x) = sin(tan-12)

Solution