#tan t = - 12/5#, t is in Quadrant 2.

#cos^2 t = 1/(1 + tan^2 t) = 1/(1 + 144/25) = 25/169#

#cos t = - 5/13# (cos t is negative, t in Quadrant 2)

#sin^2 t = 1 - cos^2 t = 1 - 25/169 = 144/169#

#sin t = 12/13# (sin t is positive)

#sin 2t = 2sin t.cos t = 2(12/13)(-5/13) = -120/169 #

#cos 2t = 2cos^2 t - 1 = 50/169 - 1 = - 119/169#

#tan 2t = (sin 2t)/(cos 2t) = (- 120/169)(- 169/119)#

#tan 2t = 120/119#