Question 669543
If {{{sin (x )= 1/2}}}, then {{{2sin (x)= 1}}}

we are looking for {{{tan(2x)}}}

use identity: {{{tan2x =(2 cos(x) sin(x))/(cos^2(x)-sin^2(x))}}}

plug in {{{sin (x )= 1/2}}}


{{{tan(2x) =(2 cos(x) (1/2))/(cos^2(x)-(1/2)^2)}}}


use identity: {{{cos^2(x)=1-sin^2(x)}}} and {{{cos(x)=sqrt(1-sin^2(x))}}}


{{{tan2x =(cross(2) sqrt(1-sin^2(x)) (1/cross(2)))/(1-sin^2(x)-(1/2)^2)}}}


{{{tan2x =(sqrt(1-(1/2)^2))/(1-(1/2)^2-(1/2)^2)}}}


{{{tan2x =sqrt(1-1/4)/(1-1/4-1/4)}}}


{{{tan2x =sqrt(3/4)/(1-2/4)}}}


{{{tan2x =(sqrt(3)/2)/(2/4)}}}

{{{tan2x =4sqrt(3)/4}}}

{{{tan2x =cross(4)sqrt(3)/cross(4)}}}

{{{tan2x =sqrt(3)}}}

{{{tan2x =1.73}}}