Use the given information to find the exact values of cos 2x

Use the given information to find the exact values of cos 2x, sin 2x, and tan 2x. cos x = sqrt 2/7. 3 pi/2

cosx=sqrt2/7 and x lies in forth quadrant

here adjacent=sqrt2 and hypotenuse =7

therefore opposite= sqrt(7^2-sqrt2^2 )=sqrt47

sin theta=opposite/hypotenuse

sin theta is negative in fourth quadrant

sinx= -sqrt47/7

cos2x= cos^2x-sin^2x= (sqrt2/7)^2 -(-sqrt47/7)^2=2/49 - 47/49=-45/49

sin2x=2sinxcosx=2(-sqrt47/7)(sqrt2/7)=- 2sqrt94/49

tan2x=sin2x/cos2x= 2sqrt94/45