How do you find the values of ##sin 2theta## and ##cos 2theta## when ##cos theta = 12/13##?

Get first the value of the of the opposite side fo get ##sin## and use the Double Angle Formula.
##costheta = 12/13##
##c^2=a^2+b^2##
##13^2=a^2 + 12^2##
##a^2=13^2-12^2= 169-144= 25##
##c= sqrt25 =5##
##sintheta = 5/13##
##sin2theta = 2sinu cosu =2(5/13)(12/13)= 120/169##
##cos2theta=cos^2u – sin^2u = (12/13)^2 – (5/13)^2= (144/169) – (5/169)= (144 – 25)/169 = 119/169##