Question 737549
Use the given information to find cos 2x, sin 2x, and tan 2x. (Enter your answers in exact form.) 
cos x = sqrt(2)/7 ,3&#960;/2 < x < 2&#960; 
a)cos 2x 
b)sin 2x 
c)tan 2x 
***
let O=opposite side
let A=adjacent side
let H=hypotenuse
..
{{{cos(x)=sqrt(2)/7=A/H}}}
{{{A=sqrt(2), H=7}}}
{{{O=sqrt(H^2-A^2)=sqrt(49-2)=sqrt(47)}}}
{{{sin(x)=O/H=sqrt(47)/7}}}
{{{tan(x)=O/A=sqrt(47)/sqrt(2)}}}
...
{{{cos(2x)=cos^2(x)-sin^2(x)=(2/49)-(47/49)=-45/49}}}
{{{sin(2x)=2sin(x)cos(x)=2*sqrt(47)/7*sqrt(2)/7=2sqrt(94)/49}}}
{{{tan(2x)=(2tan(x))/(1-tan^2(x))=(2sqrt(47)/sqrt(2))/(1-47/2)=(2sqrt(47)/sqrt(2))/(-45/2)}}}