Question #c528c Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer sankarankalyanam · Stefan V. Sep 20, 2017 #(2 tan x)/( cos x)# Explanation: #1 / (1 - sin x) - 1 / (1 + sin x) = (1 + sin x - 1 + sin x) / ((1 - sin x)(1 + sin x)) # {taking LCM} #= (2sin x) / (1 - sin^2 x)# #= (2 sin x) / cos^2 x# #= 2 (sin x / cos x) (1 / cos x)# #= (2 tan x) / cos x# Answer link Related questions What does it mean to prove a trigonometric identity? How do you prove #\csc \theta \times \tan \theta = \sec \theta#? How do you prove #(1-\cos^2 x)(1+\cot^2 x) = 1#? How do you show that #2 \sin x \cos x = \sin 2x#? is true for #(5pi)/6#? How do you prove that #sec xcot x = csc x#? How do you prove that #cos 2x(1 + tan 2x) = 1#? How do you prove that #(2sinx)/[secx(cos4x-sin4x)]=tan2x#? How do you verify the identity: #-cotx =(sin3x+sinx)/(cos3x-cosx)#? How do you prove that #(tanx+cosx)/(1+sinx)=secx#? How do you prove the identity #(sinx - cosx)/(sinx + cosx) = (2sin^2x-1)/(1+2sinxcosx)#? See all questions in Proving Identities Impact of this question 837 views around the world You can reuse this answer Creative Commons License