How do you verify #(1+tanx)/(sinx+cosx)=secx#? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Bdub Nov 17, 2016 see below Explanation: #(1+tanx)/(sinx+cosx)=secx# Left Side:#=(1+tanx)/(sinx+cosx)# #=(1+sinx/cosx)/(sinx+cosx)# #=((cosx+sinx)/cosx)/(sinx+cosx)# #=(cosx+sinx)/cosx*1/(sinx+cosx)# #=(sinx+cosx)/cosx*1/(sinx+cosx)# #=cancel(sinx+cosx)/cosx*1/cancel(sinx+cosx)# #=1/cosx# #=sec x# #:.=#Right Side 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 8432 views around the world You can reuse this answer Creative Commons License