Find sin 2x cos 2x and tan 2x if tanx125 and x terminates in

Find sin 2x, cos 2x, and tan 2x if tanx=12/5 and x terminates in quadrant I.

Solution

tan x=12/5

here opposite=12 and adjacent=5

hypotenuse=sqrt(144+25)=13

sin x=12/13 , cos x=5/13

sin 2x=2sinx cos x=2(12/13)(5/13)=120/169

cos 2x=2 cos^2 x -1 = 2(25/169)-1 = -119/169

tan 2x= sin 2x/cos 2x=-120/119