How do you prove tanx tan(1/2)x = sec x- 1? Trigonometry Trigonometric Identities and Equations Double Angle Identities 1 Answer Narad T. Jul 13, 2018 Please see the proof below Explanation: Express tanx and secx in terms of t=tan(x/2) tanx=(2t)/(1-t^2) cosx=(1-t^2)/(1+t^2) secx=1/cosx=(1+t^2)/(1-t^2) The LHS=tanx*tan(x/2) =(2t)/(1-t^2)*t =(2t^2)/(1-t^2) RHS=secx-1 =(1+t^2)/(1-t^2)-1 =(1+t^2-1+t^2)/(1-t^2) =(2t^2)/(1-t^2) Therefore, LHS=RHS QED Answer link Related questions What are Double Angle Identities? How do you use a double angle identity to find the exact value of each expression? How do you use a double-angle identity to find the exact value of sin 120°? How do you use double angle identities to solve equations? How do you find all solutions for sin 2x = cos x for the interval [0,2pi]? How do you find all solutions for 4sinthetacostheta=sqrt(3) for the interval [0,2pi]? How do you simplify cosx(2sinx + cosx)-sin^2x? If tan x = 0.3, then how do you find tan 2x? If sin x= 5/3, what is the sin 2x equal to? How do you prove cos2A = 2cos^2 A - 1? See all questions in Double Angle Identities Impact of this question 6028 views around the world You can reuse this answer Creative Commons License