Prove that tan x = (sin 2x)/(1+cos 2x) . Hence find the value of tan 15° and tan 67.5° , giving your answer in term of surds in simplest form?
1 Answer
Prove
Explanation:
Reminder:
Call tan 15 = tan t
Apply the trig identity:
Since t = 15 deg (Quadrant I), tan 15 > 0, then,
Call tan 67.5 = tan t
tan 2t = tan 135 = tan (-45 + 180) = -tan 45 = - 1
Since the arc 67.5 is located in Quadrant I, then, tan 67.5 > 0,
Check by calculator.
tan 15 = 0.27 ; (-sqrt3 + 2) = 0.27. OK
tan 67.5 = 2.414 ; (1 + sqrt2) = 1 + 1.414 = 2.414. OK